Don't forget the good ol' 2X4 which measures 1 1/2X3 1/2???
In olden times (pre 1900?) lots of lumber suppliers provided 2 x 4s that were 1 3/4 x 3 3/4. The 2 x 4s then usually were a "rough cut" and generally weren't particularly smoothly finished.
In the US, into the early '50s, a 2 x 4 was often 1 5/8 x 3 5/8. The finish then was about the same as for later ones, but more consistent "thicknesses" were made necessary as plaster board replaced "lath & mud" plaster. The new smaller dimensions were pretty much what was left after the rough-sawn surface was cleaned up on the older ones.
The conversion to the current 1 1/2 x 3 1/2 was promoted as a "conservation effort" on the part of a bunch of "trade associations," but it took about a decade (or more) before all the lumber suppliers got rid of the older stock. The long transition period makes it something of a puzzle which size will be found in construction dating back before about 1955 or so. The old dimension 2-by studs were nearly always on 16 inch centers, but new ones came into fairly general use before local standards started permitting the currently common 24 inch center spacing (still allowed only in some codes), so the distance between studs may be 16" for either size 2-bys and is not a reliable indication of what size the studs are.
If you need to patch a wall in an old house, and mix in new spec studs where old ones were used, it was/is a certainty that when you nail up the plaster board somethin's gonna crack. Most remodeling carpenters "over 40" probably have learned the lesson, but the younger crowd still may be puzzled by why nothing fits when they start nailing things together, and it may take some "persuading" to get them to measure anything but the lengths they cut themselves before they concede that the 2-bys ain't all the same cross section.
Occasionally you can find "rough cut" 2 x 4s to the older "fat" dimensions. With better machines now, they can be sawed to the 1 3/4 x 3 3/4 dimensions with finish about as smooth as the usual "planed" grade. The larger rough dimensions are fairly common on "PT" (pressure treated for moisture/insect resistance for "exposed use") but this kind isn't suitable for "indoor" repairs. The "sawn dimension" ones would nearly always be "special order" for remodelling inside an old house, so the usual solution is that if you replace one stud you replace them all in that wall, or you "offset" the new stud to make one side of the wall flat, and use another stud offset the other way for the other side of the wall if you need it.
In other words, even the inconsistency isn't consistently inconsistent.