What if I get let go after turning in my resignation?

I work as a teller at a bank and I’m turing in my 2 week notice today. It’s too much stress while I’m going to school and there are some other issues that are causing me to make mistakes when I normally wouldn’t.

1. If I turn in my notice and they tell me to just go home, can I still tell my next employer that I quit (since I technically did)?
2. If I turn in my notice and they let me work for awhile and then “fire” me, can I still tell my next employer that I quit?

I really don’t want getting fired to be on my record, but I know this situation happens a lot.

If I do get let go and put them on my resume but don’t list my boss as a reference, what can they legally tell a future employer that calls them about me?