You are correct that "two-by" lumber is standard fare for ceilings. What you're missing is that "two-by" lumber is actually 1-1/2" wide.
1-by is 3/4" wide.
2-by is 1-1/2" wide.
4-by is 3-1/2" wide.
Other sizes, subtract 3/4".
And manufacturers don't make products that require 2" wide studs. That would imply some sort of pre-war construction using rough-sawn timbers.
In the early days, a 2x4 was milled 2" x 4". Then it was run through a jointer to make one side flat, then (using the jointed side) a planer to make the other side parallel to the first side, then more passes through the planer to make both sides smooth. Same thing in both axes. Early experience was that rough-cut lumber was irregular enough that 1/2" of material would be used up in all this jointing and planing. So the target "finished" size was the finished timber was 1-1/2" x 3-1/2".
Contemporarily, mills have gotten better at their game, and are able to rough-saw the lumber more precisely, so they're not really wasting 1/2" anymore.