I understand that not many films use a different formula for the actual coating.
There might be a problem here with nomenclature.
The emulsions do need to be adjusted between the formats, due to the differences in substrate and anti-halation.
And Charles' observation about enlargers is interesting.
I'm wondering though if the differences may be more general - that the target contrast for some of the 35mm emulsions may have traditionally been different than the the target contrast for some of the 120 emulsions.
Of course, one wrinkle that can be found in some of the Kodak emulsions is the fact that there were different, similarly named films in the two formats. For example, in my 1970 edition Kodak Darkroom dataguide there is Plus-X Pan Professional in roll film sizes and Plus-X in 135 and they required different development. In contrast, Tri-X Pan and Panatomic-X were available in both formats, and the development recommendations are the same.