MG2 is the V6 5 speed that was used in almost all GM FWD V6's (i.e. the transmission you have now)
MY5 and MU1 are versions of this trans that had different ratios. They were used in a few oldsmobiles.
The other differences include VSS type and clutch throw out mechanism, but other than these minor items, they're all interchangeable.
What year was your TDC engine made? Depending on the year, Kalifornia may not allow you to use a manual trans.
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'87 Fiero GT: Northstar, Getrag, TGP wheels, rear sway bar, rod end links, bushings, etc.
'90 Pontiac 6000 SE AWD: Leaking ABS unit fixed, load levelling rear suspension fixed, still slow