Hey, I was reading a bit about the October Revolution and I had a hard time finding an explanation of this question that would make sense to someone, like myself, who isn't familiar with the particulars of Socialist ideology.
Both were factions of the Russian Social Democratic and Labour Party (RSDLP), the key Marxist party of the late Tsardom. The 'split' happened at the party's Second Congress in 1902 but I won't go into a huge amount of detail on the pre-1917 shenanigans between the two. That's partly because I find those years of factional politicking intensely boring and partly because I feel that the differences between the two pre-1917 are often overstated.
There were plenty of spats and flare-ups between the two factions - eg on underground organisations, the approach to Duma elections or just personality clashes - but these were rarely major and the parting of ways was never complete. As late as 1917, for example, in many Russian regions the RSDLP factions hadn't formally divorced: the differences between these two groups was considered more a concern of an exiled leadership than the cadres on the ground.
To illustrate, the essential differences between the two are typically given as:
That's been challenged recently by the likes of Lars Lih who argues that WITBD? has often been misinterpreted as far more elitist than it actually was (Lenin Rediscovered). James D White emphasises both that Lenin's membership rules were accepted by the RSDLP by its Fourth Congress 1906 and places the division in the context of the myriad other groupings within the party, such as the national caucuses (Lenin: Practice and Theory of Revolution).
Basically, this wasn't a simple Bolshevik/Menshevik split. Besides, this becomes somewhat moot in 1917 when the Bolsheviks did come to constitute a mass party, far from the caricatures of a small band of 'professional revolutionaries'. Whatever Lenin was arguing in 1902 regarding party structure was not particularly relevant in 1917.
That changes in 1917. Following the February Revolution, the Menshevik leadership (most obviously Tsereteli and Dan) strike an increasingly close and supportive relationship with the Provisional Government. This was in line with the pre-revolution Menshevik assumption that the role of the Social Democrats lay in supporting the new 'bourgeois' regime (as Russia was considered too backwards for socialism). In this the Mensheviks hewed relatively closely to their pre-war doctrine of the post-revolution order being essentially bourgeois.
In contrast, Lenin shocked everyone on his return in April by insisting that the Social Democrats move to immediately oppose the Provisional Government and form an exclusively Soviet government. The logic was that Russia could proceed directly - more or less, via a period of 'state capitalism' - to a socialist revolution. This was a complete departure from Marxist orthodoxy and enough to earn Lenin abuse as a 'semi-anarchist' (eg Sukhanov's Personal Record). But he carried his faction with him and put clear distance between the two groups in that critical year.
So 1917 is when the real differences open up, when the Bolshevik and Menshevik conceptions of the revolutionary process become not just irreconcilable but actively opposed. But this, I feel, was less a product of some Great Schism that went back to 1902 and more a product of the concious choice of Lenin to step into opposition in April 1917. It was also at the time in which conceptions of the party itself, ie how it should be organised, ceased to matter (in practice, if not rhetorically).
It's also worth briefly stressing that both Bolsheviks and Mensheviks benefited post-1917 from encouraging the view of a firm split, on both ideological and organisational grounds, that went back to 1903. Many of the early histories since have followed that basic narrative. This hasn't really been corrected: most of the dedicated works on the pre-revolution RSDLP were written during the Cold War and this form of pure political history has dropped somewhat out of fashion since then.
Let me know if that doesn't answer your question. It's late here and I'm happy to revisit with a clearer head tomorrow.