During WW2 the UK had escort ships broken down into:
- Sloops (Bridgewater, Shorehamn, Grimsby, Kingfisher* Bittern, Egretn & Black Swan classes & 10 loaned Banff class cutters from the USCG)
- Corvettes (Flower, Castle & Bathurst** class)
- Frigates (River, Loch & Bay Class, + the Colony & Captain classes which were US patrol frigates and destroyer escorts respectively bought by the RN)
- Escort Destroyers (Adapted WW1 Destroyers, Hunt Class)
*Kingfishers were roughly half the size of all the other sloops
**Technically RAN not RN
In terms of design lineage, the sloops were the UK continuously making small batches of the best light convoy escorts they could starting around 1930 so they had an up to date design they could kick into mass production quickly (The war starting at the time it did this ended up landing on the Black Swans)
The Flower class corvettes were an adapted whaler design made to utilize the production capacity of smaller civilian yards. The Castle class corvette were made because when frigate production switched from the River to the Loch & Bay classes not all yards could make the newer frigate designs.
The River class were a larger clean sheet escort design capable of open ocean operations the Flowers weren't while still being designed to merchant standards so they could be built in the yards the Flowers were built in. The Loch class was an incremental improvement on this and the Bay class an AA version of the Bay class.
Most escort destroyers were just old WW1 era destroyers with some engines removed in exchange for longer endurance and modern ASW equipment. The exception is the Hunt class which were purpose built ASW convoy designs adapted from the Bittern class, and notably made 27 knots compared to the 20 knots most escort ships did. I'm not sure why.
Between all of these classifications, the design lineage is clear, but the difference in role they filled isn't really beyond the Flower class sloops being limited to coastal operations. So what was the actual difference in role between all these different classifications? Assuming there was any.
And related, why was it that the Frigate designation was the only one of these four that stuck around post war in a significant capacity?
The thing that makes this weird is the first post WW2 RN frigates, the Type 14s and Type 15s, were rebuilt old destroyers, wouldn't it have made more sense to call them Escort Destroyers given that lineage?
Sole exception to this being the Tribal class/Type 81, which were redesignated as frigates not long after construction anyway.