Menshevik means one of the fewer (minority); Bolshevik means one of the more numerous (majority).
Lenin created the term Menshevik during one of early Congresses of the Russian Labour Party, to characterise the minority that opposed his position on a number of issues. The term Bolshevik (you find the same root in the name of the Bolshoi Ballet = the Great Ballet), implying the opposite or the greater number, came as a journalistic consequence.
A part the specific issues that triggered the split of the Labour Party just before the Odessa uprising of 1905, the differences between the two were the attitude towards the Socialist Party and the landed peasantry. The Mensheviks preferred a mujik oriented policy while Lenin believed in the necessity to stimulate industry over agriculture.
With the harshening of the two positions, and the reaction of the Russian aristocracy joining the Mensheviks, the quarrel drifted into open war.