This common name refers to only one class.
These are pretty much always called Leeches.
The subclass Hirudinae in the class Clitelatta contains all leeches. Leeches are occasionally found naturally in the drift in trout streams, although I've never heard of them being present in such numbers that they're a major component of the trout's diet.
They make great models for streamer flies because they're so large and ambiguously lifelike, and it's easy to make a little clump of feathers look quite a bit like a leech.