Mouse trap: "egérfogó".
What does a mouse trap do? It does not go after the mouse. It just grabs, or catches (or traps) the mouse.
The game of playing tag: "fogócska"
Tag, you're it: "te vagy a fogó"
Catch of the day: "mai fogás"
But when you are fishing with a pole, and the fish is biting the bait: "kapás van"
To catch a criminal: "elkapni", "elfogni"
Anyway, it may be best to learn these on a case by case basis as there does not seem to be a clear one to one relationship between catch/grab and elkap/megfog. Especially with these variable preverbs in Hungarian.