Before WWI, social democracy was close to a synonym for Marxism. Over the 19th century there was a long period of consolidation between socialist and workers parties, cultural organization and trade unions, eventually coming together across Europe in the Second International.

With the exception of anarchism, which had split into its own movement during the First International, the entire spectrum of socialism united into the SI, preferring to debate strategy within the same organization than to split into tendency-based sects the way leftists do today. For instance, in Germany three (broad, fluctuating) factions emerged—a left represented by figures like Rosa Luxemburg and Karl Leibknecht which advocated for mass strikes and insurrection as immediate tactics to overthrow the state; a right represented by figures like Eduard Bernstein which pushed to form coalition governments with liberals to better the immediate conditions of workers, leading to the gradual evolution of capitalism into socialism; and a centrist majority represented by figures like Karl Kautsky and August Bebel which believed socialists should act as an opposition within parliament while building up institutions like unions and social clubs to gradually win workers to revolution without playing their hand too early.

The shift toward social democracy as a specific, anti-Communist tendency emerged for two reasons. The first was the gradual development of a bureaucracy within both the social democratic parties and the trade unions, which held disproprotionate weight because of its permanent and full-time position, and tended to be a conservatizing influence on the party, marginalizing the radicals and bypassing the centrists. This become a hard-right tendency represented by figures like Friedrich Ebert, who went on to become President of Germany in 1919 and ordered the execution of Rosa Luxemburg.

The second was the first World War. The Second International was an international organization which had repeatedly passed anti-war resolutions, but in most European nations, its elected officials voted in favor of the war or took a neutral stance that supported peace on paper but opposed anti-war action. This made the entire premise behind the organization incoherent, and made maintaining a functional organization across militarized borders incredibly difficult.

This changed the nature of the (again, already fluid and inconsistent) left-center-right framework above. The right (which wasn't necessarily made up of the same people in the original, reformist right like Bernstein, but relatively newer figures like Ebert and the union bureaucracy) tended to support their own nations in the war, while centrists like Kautsky supported a negotiated peace. A new far left, including Luxemburg and the Bolsheviks (who tended to align more with Kautsky pre-war), began to emerge, advocating not just for peace but to "turn imperialist war into civil war," organizing anti-war demonstrations and agitating for soldiers to desert and turn on their officers. This divide gradually frayed the movement, leading to most of the social democratic parties splitting.

Once they had taken power in 1917, the Bolsheviks changed their name to the Communist Party to disassociate themselves from their former comrades and reclaim the legacy of Marx, who had used the term for himself. They began organizing like-minded parties in other nations into a Communist International, intentionally excluding those who had supported the war and retained the branding of social democracy.

In short, socialists before the war were usually united into a single national organization which was then affiliated to the International, but divisions over World War I made this a practical impossibility. The Bolsheviks reclaimed the term Communism, which had fallen out of use, as a branding tool to distinguish themselves from pro-war socialists, who retained the term social democracy.

A difference of optics, mostly. 'Social democracy' is considered a moderate socialist approach today, in the political environment dominated by legal equality and democracy. But in the late 19th-century Russian Empire, the whole notion of modern democracy that required abolition of classes, dissolution of the monarchy and transfer of power into the hands of people who would have an equal right to vote was easily seen at least as revolutionary as hardline communism is considered to be in modern Europe or America. Please note that today, 'social democracy' generally means support for the democratic institutions, capitalist economy that generates revenues, and interventionist welfare policies that protects interests of common citizens, all of which is more or less aligned with the mainstream policies of most modern countries. But in 19th-century Russian Empire social democracy meant the support for the complete destruction of the existing system and of the very ideological tenets of the latter (such as the assumption of the supernatural mandate of the monarch), radical change of the legal system, and dispossession of the substantial part of the society.

It is also certainly not a matter of translation. In Russian, the party was called Российская социал-демократическая рабочая партия that directly translated to 'Russian Social-Democratic Worker Party'. It should be noted however, that the term 'social-democratic' is largely a result of the party's origins. Some of the founders of the RSDLP, including Georgiy Plekhanov belonged to the organization Земля и Воля (Land and Freedom) that originated among the so-called 'narodniks' who postulated a political revolution based on the liberation of peasant class. The reforms in the 1860s caused the organization to cease its operation, as a lot of members believed that the government begins the changes they envisioned. When this proved to not be the case, the organization re-emerged, postulating transfer of all land to peasants who were to operate through local governments based on democratic principles. Again, the organization was short-lived, as the differences related to the methods caused 'Land and Freedom' to break into the Will of the People (rus. 'Народная воля', also a homonym meaning 'Popular Freedom'), favouring terrorist actions, and Black Division (as in 'breakup', rather than a military unit) that favoured the 'organic work' and political education among the masses. The first organization, although managed to successfully assassinate several high-ranking officials and attempted to kill the Tzar, ultimately ceased to exist. Members of the Black Division, for their own safety moved to Geneva, where they founded a new organization called 'Work Liberation' that is considered the first Marxist Russian political movement. The term 'social-democratic' was also popular among other Russian parties and organizations, such as 'Social-Democratic Society' founded by Mikhail Brusnyev in 1889, 'Party of Russian Social-Democrats' founded in 1883 by Dimitri Blagoyev or 'Alliance of Russian Social-Democrats Abroad' (also founded by Plekhanov). All these organizations thought that the democratic elements are necessary for the socialism to succeed, as they could not have envisioned any liberation of workers and peasants without dissolution of the absolutist monarchy, and thus a lot of their ideology was in line with various democratic parties that formed in absolutist countries across Europe. The division between radical and moderate factions (usually along the lines of revolutionary internationalism versus evolutionary liberalism) became more pronounced since 1914 and the onset of the Great War.

In general, as already said by u/piscespastel , the term 'social democracy' was often treated synonymous with 'socialism' or 'marxism' as many parties and organizations of such profile were modeled after the Social-Democratic German Party established in 1869 by August Bebel and Wilhelm Liebknecht. The differences between 'socialism' and 'social democracy' began to form in late 1880s, largely due to the views of Eduard Bernstein, who stressed that development of capitalism might help also the workers and the gradual democratization was gradually abating the class struggle. Thus, in his opinion, the optimal course of action was to support a grassroots organizations that would utilize the democratic mechanisms to further the cause of the 'common man' through evolution rather than revolution. But still, most socialist parties of the era, regardless of their name, put stress on self-governance of the people, abolition of formal classes, republican government, universal suffrage and self-determination of the nations, statements still revolutionary in absolutist monarchies. Please note that most if not all elements mentioned above were included in the 'minimal program' of the RSDWP formulated during the 2nd Party Congress in 1903. Also, after the 1905, the party Central Committee was far from unified, with multiple fractions discussing the future of the political organization, with 'Liquidators' opting for complete cancellation of illegal activity and focusing on the political work through Duma, 'Rejecters' claiming the exact opposite, 'God-Builders' (Christian positivists) or 'All-Regioners' that attempted to reconciliate squabbling factions. Even after the revolution, RSDWP was supporting the ideas of republicanism, openly stating that it does not support any sort of 'dictatorship of proletariat' that would involve any sort of actual dictatorship of the minority over the majority.

Eventually, the more radical faction led by Lenin gained prominence, and although it cooperated with less radical social democrats during the war, as was the case of e.g., Zimmerwald Conference in 1915 and ultimately broke out of the RSDWP in 1918 and formed the Russian Communist Party (since 1925 called the All-Russian Communist Party), decidedly severing ties with now distinctly more moderate socialists who quickly became sidelined and almost completely eclipsed since early 1920s.

So, to sum it up, the social democracy mentioned in the name of the RSDWP was definitely revolutionary movement, as far as the absolutist monarchies dominating Central and Eastern Europe in late 19th century are concerned. But even then, some factions within the party still radicalized after the 1905 and although they have chosen to operate under the same banner, they eventually parted ways as the differences of both personal and ideological character became too severe to maintain cohesion.