I'm not aware of specific definitions, but in the context of the US, a lawn often has regular applications of fertilizer and herbicides to promote the growth of a small number (often a single) species of grass. This also requires more regular watering, as the grasses tend to be less drought resistant.

A meadow, or natural lawn, or whatever you want to call it would be a mix of grass, clover, and other "weeds". It wouldn't require anywhere near as much chemical treatment (if any) and could be mowed and watered far less often. To me, it would also be allowed to grow long enough to flower, to promote pollinating insects.