First please note that the following descriptions are limited to the case of fully austenitic microstructure (water-quenched one).
The Hadfield steel was designed by tuning the chemical composition to be approximately Mn:C = 10:1 in mass and to contain approximately 1 mass% C or higher. In contrast, the TWIP steel was designed by optimizing stacking fault energy for deformation twinning (20-40 mJ/m2). Therefore, in general, the austenite of Hafiled steel is stabilized by mainly carbon and secondary Mn. This design concept resulted in extraordinary strain-age hardenability by solute carbon, in addition to twinning. Therefore, the wear resistance is very high. On the other hand, TWIP steels must show deformation twinning as the primary deformation mechanism, and therefore the stacking fault energy must be reduced by composition selection. In this regard, carbon "increases" stacking fault energy, and hence carbon was not selected as the primary element. Namely, Mn and Si was selected for the prototype TWIP steel. After the prototype, Fe-Mn-C TWIP steels were designed based on stacking fault energy calculation. This history provided two kinds of high-Mn steels with similar compositions of Fe-Mn-C. After optimization with these concepts, the chemical compositions of Hadfield steel and TWIP steel were Fe-12-14Mn-1.0-1.2C and Fe-18-22Mn-0.6C in the ternary system. However, as you know, both steels show significant age-hardenability and twinnability. Therefore, as you can see here, somewhat they are similar to each other. For instance, Fe-22Mn-1.0C can be called as both Hafield steel and TWIP steel. I hope this info is helpful for you.