Wait(), will cause to run potentially async code in sync manner. await will not.
For example, you have an asp.net web application. UserA calls /getUser/1 endpoint. asp.net app pool will pick a thread from thread pool (Thread1) and, this thread will make a http call. If you do Wait(), this thread will be blocked until http call resolves. While it is waiting, if UserB calls /getUser/2, then, app pool will need to serve another thread (Thread2) to make http call again. You just created (Well, fetched from app pool actually) another thread for no reason, because you cannot use Thread1 it was blocked by Wait().
If you use await on Thread1, then, SyncContext will manage sync between Thread1 and http call. Simply, it will notify once http call is done. Meanwhile, if UserB calls /getUser/2, then, you will use Thread1 again to make http call, because it was released once await got hit. Then another request can use it, even further more. Once http call is done (user1 or user2), Thread1 can get the result and return to caller (client). Thread1 was used for multiple tasks.