Plaster to drywall joint question.
I have done a few demos where the type of backer you're referring to was used for plaster. It's like the "gyp" board sheathing used years ago (like my house) and it's usually 24"x8'. I haven't seen it in a long time, but I thought it was 1/2" thick, like the exterior sheathing. (And as I recall it had holes in it to let some of the plaster push through??) Might have been 3/8" or 1/4" though. And as stated above, setting compound is the answer to your transition question.....
If you can read this, thank a teacher. If you can read this in English, thank a soldier. Support our troops.