I've seen that there are different groups like $SU(2)$ and $SO(3)$ with isomorphic Lie algebra. I know that putting the elements of the linear algebra in the exponential function gives the group elements, in this case I don't understand how it's possible that two isomorphic linear algebras gives different groups
Does it mean that when I put two isomorphic group in the exponential function I can obtain two non isomorphic groups?