What is the difference between an Aryl Halide and a Vinyl Halide?
No, aryl halides are not a type of vinyl halides.
A compound is called an aryl halide when it contains a halogen group directly attached to an aromatic system. For example,

Whereas a compound is called a vinyl halide when it contains a halogen group directly attached to a doubly bonded carbon atom. For example,

The double bonds in an aromatic system are not the same as the aliphatic double bonds. They differ quite a bit in terms of electron density and thus there derivatives behave very differently is many circumstances.
The term phenylic halide doesn't exist but a very similar term phenyl halide exists which is a subset of aryl halides family.
An aryl halide can be called a phenyl halide when the aromatic system of the compound is specifically the phenyl system($\ce{-C6H5}$). For example,