At the same time has 4 different meanings across 2 categories:
overlapping in duration
"concurrently with the conference an exhibition of things associated with Rutherford was held"
"going to school and holding a job at the same time"
despite anything to the contrary (usually preceding a concession)
"although I'm a little afraid, however I'd like to try it"
"while we disliked each other, nevertheless we agreed"
"he was a stern yet fair master"
"granted that it is dangerous, all the same I still want to go"
Simultaneously.