Hmm, I'm no fishing man, but I think that when you Trawl you are using a big fishing boat that pulls a very long net on the ocean. When you troll, you are rowing a small boat (in a lake perhaps) with a special kind of fishing rod ...
Yes, you are of course correct. I've never heard about trolling as a fishing method before, only trawling, but looking it up on the net I see that trolling is indeed a fishing method.
