> Surely 'density' is a measure of stuff per area?

Not really, the normal definition of density is mass per volume. If you mean something else (like storage capacity per area), it needs to be specified.

You get linear density (for density along a line) and also volumetric density (scales with volume). So you're basically making it clear how many dimensions are important to your measurement.

https://en.wikipedia.org/wiki/Area_density

Areal is the adjective form of area.