there are more than 3 types of axles for T-series diff's, this is mainly in the length of the axle, but there's spline and bearing differences also.
a T-series LSD will NOT fit a KE70 Japanese or Australian.
As for putting a TRD LSD into a T-series diff, if it's the right LSD for that diff there's no problem.
Zenki and Kouki refer to AE86 axles only, early and late, and the splines are 24 and 25.
david: the AE86 disc brake diff will bolt straight in, the only thing to change is the drive shaft flange, make sure if you buy one of these diff's it has the hand brake cables with it.