Hello, what's the difference between strictly speaking and properly speaking?

See a translation

Strictly speaking is used to indicate that whatever is being said is to be interpreted to the most literal degree/some rule is being applied in the most literal sense. That explanation probably makes no sense, so here’s an example:

If I get into a car accident and I’m not a great person, I might say something like:
Strictly speaking I didn’t hit XXX, I hit her car.

If I send a paid bill in the mail on the due date and it gets to the company that charged me after the due date, I could say:
I sent my payment on time, strictly speaking. The mail just took too long.

Properly speaking sounds strange and not an everyday term (at least where I’m from in the US). From an online search it seems to mean the exact same thing as strictly speaking. In that case there really is 0 difference and you’re free to use whatever you like.