A Cloud phone system is basically a telephone system delivered through the internet
“Before the advent of VoIP, phone systems were all based on the public switched telephone network (PSTN) – the copper wires that made up the global phone network. It was still possible to have a cloud based phone system in the PSTN cloud, but the real use of the term came as part of the growing trend toward cloud computing and cloud services toward the end of the first decade of this century.”
In order to be classed as a Cloud phone system, the process has to be able to make and receive calls through the internet. Also, as it is most often used by businesses, it has to be able to route calls to specific extensions. Lastly, it has to be able to offer certain specific applications, like call recording and voice mail.