First, some technical explanations to lay out an overview of what you're looking at.
PSTN, POTS and PBX
The traditional model for voice communications is the PSTN, or Public Switched Telephone Network. This is, essentially, the phone company -- its infrastructure, cables and so on. It handles your phone calls, and has its own range of technologies for ensuring that your call gets through properly.
Although this is a slight over-simplification, the basic model of the PSTN is a mainframe/terminal scenario. The switches and exchanges of the phone company provide all the features and functionality of your call service. Your telephone is just a dumb terminal, with barely any inbuilt features of its own. Even phones with funky buttons for call waiting, call forwarding and placing calls on hold are completely reliant on those features being supported at the switch. The switch provides everything to the phone (including its power), and every signal which comes from the phone, from the keys pressed to your voice, has to be managed and interpreted by the switch.
Every phone connection, therefore, has to connect directly to the switch. In low-density situations like a residential connection, the individual connections back to the switch are called lines. In situations where a greater number of phone connections are needed, like offices, it's expensive and impractical to connect multiple lines to the exchange so a PBX, or Private Branch Exchange, is used instead. This is a smaller switch mounted and installed in-house, with a line going back to the main exchange called a trunk. PBXs have the advantage that all internal calls do not have to route out of the PBX and back to the exchange, so the phone company is not involved and the calls are free.
However, the basic model still applied -- the PBX carries all the functionality and the phones are just dumb terminals.
The simplicity of the switch/terminal system has enabled voice communications to be reliably serviced over fairly dated infrastructure. A phone line connected to a house in the 1970s is still perfectly viable. However, it also means that any new features or upgrades have to be applied to the switch, and this often means new, dedicated and expensive hardware. This doesn't really impact home users (until the bill goes up with a new -Service Fee" attached), but when businesses wish to upgrade PBX functionality, dollars can quickly vanish.
VoIP vs IP Telephony
These two phrases do get bandied about a lot -- to the extent that sometimes they're interchangeable and sometimes meaningless. The definition that makes the most sense is this:
- Voice over IP describes the technology required to run voice communications over an IP network
- IP Telephony describes the features and capabilities open to you now that you are running VoIP
To be honest, the only thing which matters is that the definitions makes sense in the context in which it's being used, and that it's used consistently. This article will only be talking about VoIP, using the definition outlined above.