Hosted telephony is cloud-based, rather than onsite and is accessed via a remote location. More information can be found here to answer ‘what is hosted telephony?’.
The remote location is a Hosted PBX (Private Branch Network) which is accessed through an internet connection. A Hosted PBX can also be referred to as a Virtual PBX and saves businesses on installation and maintenance costs of Hosted Telephony systems.
Hosted telephony and hosted PBX are not the same but can be interrelated.