I often use the terms corporatism or plutocracy to describe our system. I like your distinction between capitalism and free enterprise. It’s really good to define terms—ideally neutrally—to have better discussions.
Sadly, plutocracy is loaded term but it’s hard to find a word to describe a system with elective government awash in corporate money. Thus, corporatism.
I also think defining the terms earned income and unearned income clarifies many things.