What would the difference be between "pure" Anarchism and Anarcho-Syndicalism?
I don't think there is any "pure" anarchism, really, and it'd be a mistake to imagine that "anarchism without adjectives" (as it's called) represents a more anarchist-y anarchism simply because it eschews labelling, even if a lot of its proponents seem to imagine it does.
It'd tend to think of anarcho-syndicalism is a particular mode of anarchism, rather than a qualification by or hybridisation with syndicalism. And, ideally, a suppose, a particular mode of syndicalism, rather than a qualification by anarchism.
My personally feeling is that, historically and today, a lot of anarchists put too much weight on the label "anarchist", as if it were some binding ideal rather than a simple descriptor, which means they spend far too much of their time listening to the ideas of bomb-lobbers, gutter-punks and postmodernists (and which is worse?) simply because "we're all anarchists",, while remaining closed off to useful thought that happens to carry an over-strong whiff of Marxism. But, that's not always the case, and since 2008, anarchists seem to be taking class seriously again- which in practice often means, people are coming to anarchism fresh, without the patience for the old hobby-horses ("well, sure, they're striking, but are they
vegan?"), or for that matter with the archaic theories of the paleo-Marxist sects.