Why are some of the supports on bottom of a lego piece hollow, and other are solid? I've added an image of me holding two 1x3 bricks, one has solid supports (not sure the technical name...) and the other has hollow supports.

Does anyone know the reason why they are different? Other than that, they are identical and from what I know they were purchased at the same time (I didn't buy them).
Almost assuredly it is a move to reduce the amount of plastic used. It may seem inconsequential, but adding up hundreds of millions of these makes for a ton of savings. The same thing goes for the brick walls, but not in the case of the ones you show here. I haven't seen it in any 1x bricks, but in most 2x bricks these days, the walls are a tiny bit thinner (perhaps the cause of many complaints of translucency) but with little ridges there the studs touch to keep clutch at appropriate levels. One might guess that this new wall would reduce the number of times a brick will accept a stud before losing reasonable clutch power.