What is the difference between aryl and alkyl phenyl?

I'm assuming you mean "alkyl phenyl" vs. "aryl", rather than "aryl phenyl" vs. "alkyl phenyl", because "aryl phenyl" seems redundant.

I interpret "alkyl phenyl" as the one on the left here:

An example of an alkyl phenyl you might see often in class is a benzyl group, like in benzyl bromide (bromomethylbenzene). For this group, ##n = 1##. Then change the squiggle to an ##R## group of your choice.

The one on the right actually very closely resembles a phenyl group, which is a type of aryl group. Just change the squiggle to an ##R## group of your choice.

But aryl doesn't have to be phenyl because it's an umbrella term. It can also be indolyl or thienyl, for example.

You can see an indolyl group in tryptophan, the only natural aromatic amino acid with two rings.

You can also see a thienyl group on ##beta##-2-thienylalanine. Apparently it's a phenylalanine (Phe, F) antagonist.

So, you can simply think of aryl as some sort of substituent derived from an aromatic ring.