> Is there really a difference in how “should have” and “should’ve” are pronounced?

I sure hope so, one's a contraction and the other is not...

Likely gp meant "should of" and "should've."

Indeed

What I'm saying is that people in certain regions actually say "should of" instead of "should've".

And yes, there can be and often is a difference between saying "should've" and "should of".