The term "Bolshevik" pre-dates the October Revolution. Since you mention the Mensheviks, I assume you're at least passingly familiar with the split between the two factions within the Marxist Russian Social Democratic Labor Party. The ideological split happened at the Second Party Congress, where the Bolsheviks won a majority of debates and decisions on the issues being discussed at the Congress, and that is where the "majority" part of the name comes from.

Also, a tiny nitpick, your translation of Bolshevik and Menshevik would be more accurate if you said "one of the majority/minority", as Bolshevik derives from the Russian "bolshinstva" and "menshistva" ["majority"/"minority" as you stated] and the specific terms were the official names of the members of those organizations. However, nobody would have any trouble understanding what you meant...just for your own knowledge :)

Edit: Sorry, I missed your question about what the Mensheviki held as their principles - I can explain that as well. You're partially right about the statement on Menshevik beliefs, but I am going to briefly explain it for anyone else interested.

There were many key issues that caused the two groups to split. These included the failed 1905 Revolution and the aftermath, philosophical and ideological differences with regards to class leadership, class alliances, and two different interpretations of Marx's historiography method of analyzing history through the lens of a society that has its history/choices/decisions determined by that society's mode of production (in Marxist terms, how the society's potential maximum production interacted with what Marx and Engels called the "relations of production" The relations of production boils down to the collective social agreements and relationships that people have to enter into in order to survive and argues that because this is mandatory, the proletariat will always be at a disadvantage against the bourgeois/capitalist class due to the inherent stability of the economic system in question.

The Mensheviks were much more moderate than the Bolsheviks and were more cautious in how they wanted to approach the inevitable revolution of the international working class. It should be pointed out that despite their ideological and philosophical differences, the leaders of both parties (Lenin and Trotsky, to name the most famous) did not really view each other as enemies or treat each other antagonistically. Despite this, Menshevism was legally banned in the Soviet Union after a failed uprising at the Kronstadt fortress was put down in 1921. All Mensheviks were required to conform to Bolshevik beliefs and promote Bolshevism. When Lenin's Reds won the Civil War, many of the government officials and leaders of the new Soviet Union were Mensheviks, and Lenin handpicked Trotsky to be his intended successor after his death, but Stalin was much more conniving and cut-throat for Trotsky to be able to get around and Trotsky ended up getting an ice pick in the head for his trouble.