@ Mattyboy..In these Modern times. Destroyers are generally ships that are anti air warfare. Think Type 45 or Arleigh Burke/ With Frigates been for Anti Submarine warfare. Although even that is thrown apart by the French/Italian Frem class ships and the German Frigates and Dutch Frigates which are AAW.
I suppose the real difference is to do with politics.
Your in charge of the Navy..You ask for Destroyers.
The Minster of Defence says. He won't pay for destroyers..
How about Frigates??
You say OK..And design ships of destroyer size and budget..But call them Frigates for funding purposes.
After all You haven't bought destroyers..Have you?
That's sort of how it works..I guess.

I've never really understood the difference between a frigate & a destroyer, particularly in these modern times. One I presume has more armaments ?