Maybe I'm just too "in it" from having eaten Thai fish-sauce almost every day for many many years, but I'm not convinced that fish sauce tastes of fish any more than soy sauce tastes of soy or red wine vinegar tastes of red wine. It tastes of salt and umami and ... tastes like fish sauce.
I think you’re “in it”. I had a partner that loved fish sauce and insisted it didn’t taste “fishy”, but to me, who didn’t grow up with it and generally dislikes “fish” taste, it tastes extremely fishy.
IMO, fish sauce (and I'm picturing the red boat one my wife buys) is like manna from heaven when there's just a hint of it. Too much, and it starts to taste a little...poopy.
I use fish sauce in small amounts to make fried rice. (Also present, in large amounts: oil, soy sauce, garlic.)
It has no flavor that I can particularly detect at the end of the process. The smell when you open the bottle is overwhelming, and terrible. I wouldn't venture to sample it directly.