Can two non-isomorphic connected compact simple Lie groups have homeomorphic underlying manifolds?

Question

I often see connected compact simple Lie groups represented as surfaces.

My question is, are the underlying topological spaces of all compact connected simple Lie groups non-homeomorphic?

If this is true, could you outline the reason?

Note compactness is needed because of the counterexample (R,+) and (R^+,*). And non-simple counterexamples also exist such as U(2) and SU(2)xU(1).