That's not quite correct. The light duty 10 speed automatics (GM 10L80, Ford 10R80 and 10R100) are indeed very similar and do share some parts, though each is manufactured by their respective companies. Some parts actually have both GM and Ford part numbers on them. Those transmission were jointly developed by GM and Ford. An insider told me, FWIW, that those transmissions are actually derivitives of GM's 8 speed 8L90 with an extra gear! Maybe so...
The heavy duty 10 speed automatics are where things get a bit different. The Ford 10R140 is basically a simple scale-up of the GM/Ford JV light duty transmission. Though very few parts interchange, it works exactly the same way. GM originally considered doing the same thing with their HD 10 speed, but instead decided to go their own way with the 10L1000. The 10L1000 was done by Hydra-Matic. While there are some similarities between the 10R140 and 10L1000, there are many differences. Gear ratios are different, the 10L1000 usually doesn't start in 1st., no internal parts interchange, and some internal components are in different locations. In addition, the torque converters are completely different, and for some reason while the GM transmission fluid temp. typically runs at around 160-180 degrees even when towing, the Ford will top 220 degrees in normal driving! The 10L1000 is a Hydra-Matic, but Allison did some design consultation and verification on it, and GM paid Allison a royalty to stick their badge on it. The royalty agreement runs until 2026, and my understanding is GM doesn't want to pay Allison anymore for a transmission that is their own.
Now we can argue which one is better, the GM 10L1000 or Ford 10R140!