Transmission and gear box are the same thing on an automatic. That car should have the GM built 4T45-E transmission. There has been a few issues with these transmissions, one is a broken feed pipe inside the transmission. It isn't a hard fix, you set up a pan to catch the transmission fluid, then remove the transmission pan. You will see the feed tubes that run across the inside. The failure is that the tube breaks free at one end and you lose all forward gears suddenly. It is easy to tell if this is the issue as you can gently pull on the tubes and the broken one will move when it shouldn't. For the repair you remove and replace the tube assembly, then replace the filter, reinstall the transmission pan and fill the transmission. Then see if you now have all the gears. If the tube was broken it should be repaired.
Here is a quick video on it:
https://www.youtube.com/watch?v=53_F2j1G_GU
Sunday, June 7th, 2020 AT 2:26 PM