Hosted VoIP, also referenced as Hosted PBX, is VoIP service that utilizes the cloud to deliver phone service. Essentially, you pay a subscription fee (usually charged on a per user/per month basis) to a VoIP service provider. In exchange, the VoIP service provider gives you VoIP service without any headaches.
The Hosted PBX provider sets up the system, sets up the extensions, sets up any features you may need, troubleshoots the system, and updates the system.
With Hosted PBX, you get a complete virtualized VoIP phone system, managed by the VoIP provider.
And what about Virtual PBX?
Virtual PBX is VoIP in the cloud too.
Virtual PBX is sometimes the same thing as Hosted PBX; other times, Virtual PBX works as a call-in/call-forwarding service.