It's the difference between using mostly meetings (real or virtual), IM and phone calls versus using mostly email. If you use mostly email for your comms it is perfectly possible to be both remote and async.
Most large companies are some combination of async and sync. If you have offices in the US and offices in Europe--much less Asia--you may have some hopefully not too inconvenient real-time calls. But you'll probably do a lot of things asynchronously. (And even within an office or within a country, a lot of people travel, have customer meetings, etc. so they're often just not immediately available.
I've never heard companies say they're async though, only remote. The two seem to be conflated most of the time.