It meant "classical Marxist" to a large extent, as in someone labeled a "communist" in 1910 would have adhered to beliefs that are much more controversial in today's Marxist community than back then, most notably the idea that capitalism is a progressive force in developing countries.

Thus, if you want to have a clear idea of the set of beliefs of a Marxist, one can find the majority of them in Das Kapital and Grundrisse; for theories on imperialism, a read up on Hilferding would yield the best understanding.

In the early 20th century, communists were intent on describing the "self liquidation" of the capitalist economy (for more on this, read Lenin's theory of imperialism) whereas the latter of the century was more focused on explaining the self perpetuation of capitalism (see dependency theorists, although some of them aren't marxist, most prevalent is Wallerstein).

Indeed, the only thing that really "unites" Marxists today, with the plethora of different and strongly opposed subgroups of the ideology, is that the majority hold a strong belief in historical materialism.

The idea of Marxism has really become more of a form of polemic lens to look through history, than an economic ideology (As one can see through the lack of policy prescriptions from current Marxist intellectuals as compared to the early 20th/late 19th centuries).

If you want to share any of the positions that you were debating a "communist" would have held in 1910, I can attempt to confirm them.