For example: trout; salmon; deer.

Greetings fishterrier

I wonder (idly) is this has anything to do with the creatures concerned being edible.

"What did you have for lunch today?"
"I had fish/trout/salmon/deer"

Same as "I had whitebait/quail/chicken/beef/pork/bread", in that you could have had any number of units (whatever they may be).

This is, of course, further complicated by our having different words for meat and its source animal(s).