"Lärm" is loud, annoying noise of some kind. If you live next to a construction site or busy street, you might be bothered by "Lärm".
"Geräusch", on the other hand, can refer to any sort of sound. It could be quiet or loud, and doesn't have to be bothersome. You can use it to comment on the character of the sound, like "dumpfes/kratzendes/schwaches Geräusch".
In short, everything that you hear makes a "Geräusch", but only loud, annoying things make "Lärm".