I purchased an iPhone 13 Pro last year with Apple care pro if I trade it in this year since I receive a new/refurbished phone for the $99 fee would I receive the same kind of phone or an iPhone 14 Pro or something
Trade-in has nothing to do with Applecare+. AC+ is an extended and expanded warranty service, trade-in is getting value for your old phone to put towards a new one - which model is up to you and you pay the difference.
If you have a better condition phone due to recent replacement, you might get a better trade in value but probably equals out with deductible.
In 99.9% of cases you will receive exactly the same device (this is only if your device is not repairable). I have a friend who destroyed his iPhone X and they upgraded him to a XS because they didn’t have any iPhone X in stock for at least a month. But this very, very rarely happens.