Not necessarily. It means multiple computations could happen at the same time. Wikipedia has a broader definition [1]: "Concurrency refers to the ability of a system to execute multiple tasks through simultaneous execution or time-sharing (context switching), sharing resources and managing interactions."
In other words it could be at the same time or it could be context switching (quickly changing from one to another). Parallel [2] means explicitly at the same time: "Parallel computing is a type of computation in which many calculations or processes are carried out simultaneously."
0: https://wiki.python.org/moin/Concurrency
1: https://en.wikipedia.org/wiki/Concurrency_(computer_science)