Consequence v Assumption

To say that something is a consequence of a view or statement is to say that it is something that logically follows from that view, in other words, something that must be true. An assumption would be something that the author of an argument must agree with, and has taken to be true without proving or stating that it is true. In practice they may look similar, but I'd say the main difference is that a consequence can be true of either an argument or a set of facts, while an assumption would only apply to arguments.