at the same time

1.  Simultaneously, as in We were all scheduled to leave at the same time. This idiom was first recorded in 1526. For synonyms, see at once, def. 1; at one time, def. 1.
2.  Nevertheless, however, as in Mary agreed with her mother's criticism, but at the same time she wanted to defend her husband's views. [c. 1700]

The adjective has one meaning:

Meaning #1: occurring or operating at the same time
  Synonyms: coincident, coincidental, coinciding, concurrent, cooccurring, simultaneous

The adverb at the same time has 2 meanings:

Meaning #1: at the same instant
  Synonym: simultaneously

Meaning #2: overlapping in duration
  Synonym: concurrently