PT113B1 and PT167A1 do NOT share the same layup.
They do feel close to me, that means really nothing. As an amateur player, there are many things that I do not consider or notice in the layup. But I'd say the feel is similar, the softness and pocketing is similar, the sound is similar, the weight balance is similar. Both are TT technology.
I am not sure how Head comes up with the Mold identifiers/naming, but each of these have their own separate physical molds, there are dozens of them sitting on the Head shelves in KB and I have seen the TK113A and TK113B and TK346 separate molds.
Good question about the TK113C -- is that a separate mold? I do not know. To me, it looks identical to the TK113B mold (that is definitely different from the TK113A mold), although those are rare.
In the PT world, Head does not need to follow specific logic -- it is like a geek corner there where they experiment with many, limited quantity things. They can call it whatever they want and sometimes they do not have specific rules they follow. It is different in the TGK/TGT world where they manufacture by a third party.
On unrelated topic, that is another reason why Head could not do the mass production of the PT346.1 for example -- they only have 1 (possibly 2) mold of those, all in KB. And molds are expensive to build.
On the other hand, as an example, they do have multiple of TK339 molds in their factories in China.