Is this meditation what I've been doing sometimes? Or what is it?

Meditation can be a number of things really, its not one set thing and its often something can be done without even fully realizing. There are certain practices done a certain way and for certain purposes of course, but I would say that is a form of meditation for sure. Concentrating on your breath is probably one of the more typical ways but you don't necessarily try to not think(because in a way, thats still thinking), you just acknowledge the thoughts for what they are and focus back on the breath, and notice how a lot of the time thoughts just sort of fade into the background. You can do this with urges too, its called urge surfing and it can be pretty powerful. Depending on whether you want to increase your compassion, become more detached, urge surf, improve concentration, or a mix of all these things, that'll guide you towards certain kinds of meditations.