Got lead certified recently, but I pretty much drop a grade when climbing lead - I’m not as confident and I overgrip.
I’ve done lead falls, I know how to do 'em well, and yet… as someone who’s done top rope for many years, it’s scary not feeling the tension (however small) of a rope pulling your harness up.
Both, really. Practice falls will help for sure, but it’s always easier to commit to a voluntary fall.
Being in a situation where you’re trying your hardest not to fall is where the fall anxiety really comes out, and pushing through that is a question of practice. The first fall in a session is usually the hardest, and once you’ve taken that fall, you realize that it’s not that bad, and it gets easier to commit.