Phenyl or benzene when naming compounds
You are confused about several overlapping but mostly unrelated issues.

First, you are right that "benzyl" is the $\ce{C7H8\bond{~}}$ radical and that "phenyl" is the $\ce{C6H5\bond{~}}$ radical.  

Second, although "phenol" and "phenyl" sound almost the same, you would probably do well to think of them as entirely separate naming roots.  "Phenol" is the simplest aromatic alcohol.  Simple aromatic alcohols with other substitutions (e.g. 4-chlorophenol) can thus be named as substituted phenols.  

Third, "benzyl" and "benzene" similarly sound the same but should be treated as distinct concepts.  Substituted aromatic rings can be named as benzene derivatives, such as chlorobenzene.

Fourth, for shorthand and convenience, "phenyl" and "benzyl" are sometimes used to name substituents.  Note that IUPAC has detailed priority rules for what is a substituent and what is the base molecule, but chemists don't always follow these.  "chlorobenzene" is a correct IUPAC name, and it views the molecule as a substituted benzene.  That is, benzene is the base molecule and "chloro" is a substitution.  Chemists sometimes find it convenient to reverse their perspective, even though the resulting names would not be IUPAC-approved.  From a reverse perspective, the chlorine atom is the "base molecule", and it is substituted by a phenyl group.  Thus you could call the chlorobenzene "phenyl chloride" if you wanted to take this reverse perspective.

Lastly, "bromophenyl" ends in "-yl" and so is the name of a "radical", i.e. a substituent or fragment, not of a complete molecule.  Without any other context, I would think that "bromophenyl" was a $\ce{C6H4Br\bond{~}}$ substituent.  In contrast, "bromobenzene" is a complete molecule, derived from benzene by substitution.