It's not very similar. The fish in Worcestershire sauce is mild enough that you might not notice it if you didn't know it was there. It's vinegar + molasses + tamarind + salt + sugar + spices, with the fish just there for added umami taste. Thai fish sauce is only fish + salt + sugar, and it's unmistakably made from fish.
Agree the fish sauce itself is clearly different, but I'm less confident about the flavor profile as a whole. Maybe that's just because of the tamarind though.
Fish sauce seems plausibly one of those commonly re-invented things.