What is my wall made of?

I'm removing the tile backsplash in my kitchen to redo it. The tile is taking chunks of the wall with it that I am going to have to repair. I was assuming this would be plaster like the rest of the house (built 1928, added onto sometime before 1952) but then one chunk took out enough to a paper backing behind it. Is this cement board or something else? Should I repair it like it is plaster or another method? 

And then the adjacent wall where this lovely outlet relocation is appears to be drywall at least in this section. 

In between the years of wood slats and drywall they used a rough papered drywall product that was designed to hold plaster. Usually it is a skim coat to keep the hand worked plaster look but behind tile you may have a thick bed of plaster over it like you would over wire lath. Dig through that paper and see if you have some gypsum behind it.

I would rip it all out and put up 1/2 hardibacker or durarock.  It all depends on what you are trying to match and end up with.

Asbestos? 

If doing tile, I'd just grout it up.

It appears to me to be older style Gypsum board that was used in the 40's and 50's.   It's much like sheetrock, but heavier and also might contain asbestos.

Then again, it could be an early version of concrete backer board.

Are you putting tile back up?  If so, it can be repaired possibly even with thinset if you don't have too many spots that are "blown through".  Sort of like putting a new scratch coat up before tiling.

I know nothing much of such things, but that looks more like concrete, which brings to mind the term "Mud job"

Everything I know about such things I learned from television.