Need to check what years you have. The a4ld changed a bit over the years.
I have an 89 a4ld car and was just plain lucky to get a cheap trans that matched.
The key is how many solenoids it has. Some have only one (I think, its been 5 years) that controls the converter clutch lockup, and later ones have two, coverter clutch and od control. Your 93 has the later a4ld with more solenoids, I think.
You can pull the pan and compare them, if they match, you should be good.
You might be able to tell by comparing wiring connectors, but not sure.
The wrong one will bolt up fine, but some functions may not work in the trans, late trans in an earlier car because of no signal from the puter. Not sure if an early trans will work in a late car or not.
You also may have to figure out how to hook up your speedometer. '87-88 Thunderbirds had electronic speedos, Mustangs were cable driven. Early TC''s had cable speedos, from '83 up til maybe '86 (I think the '86 TC's actually had an '87-88 style interior and cluster)