Communists sought the destruction of the state though, not random individuals who have nothing to do with the institutionalised state.
When I was referring to destruction of states, I said "collapse with maximum internal damage", which is to say that the states would be destroyed in order to precipitate a collapse of the society, with concomitant human catastrophe.

So it's basically just what you said. Communists sought to transition - forcibly or not - capitalist societies to (Communist-run) socialist societies. Meanwhile, Islamists at the extreme perceive that they already have their society and the existence of other societies is both an active and passive threat; moreover, there is some motivation to simply accumulate as much territory and as many subjects as possible for the glory (more-or-less).