POTS is circuit-switched telephone service, which means when you pick up the phone to make a call, that call takes place over a dedicated circuit. The call data travels from your location to its destination via copper wire. That translates into strong reliability and low latency. However, only one type of communication can use that line at a time.

Today, how calls are transported has changed slightly. Telephone calls still take place over a dedicated circuit; at least until they reach the telecommunications switch that routes the call to the correct recipient. In many cases, however, when call data reaches the telecommunications switch, it's digitised and moved to the Internet to be transported down the line. Then, when your call reaches the switch nearest its destination, it's converted back to analogue data and delivered to the recipient.

That slight change in how call data is delivered from one location to another may be a big contributor to the recent drop in long distance costs. The reason for that is the ability to deliver more than one call at a time. A dedicated circuit can deliver only one call. So, for instance, if you made a call using the old analogue service, the only call that could travel along the circuit you were using was your call. Only when you hung up and freed the line, another call could use that path.
When call data is sent via the Internet, however, it's compressed to a much smaller size (and the Internet is a much larger pipe), meaning that more than one call can travel the same path. That's what makes VOIP such an attractive service.

VOIP, on the other hand, doesn't transport call data to a switch before digitising it and taking advantage of the resources of the Internet. Instead, VOIP uses packet switching to immediately convert call data to digital information, which is broken into small packets, and delivered via the Internet.
At the receiving end, the small packets of call data are reassembled and, if necessary, delivered to the receiving party via the nearest POTS switch. If the receiving party happens to also be using VOIP, there's no need for the data to ever enter the POTS system.

Ultimately, the results are the same. You make a call that travels to the recipient via the most economical means possible. The biggest difference is usually how the call begins and ends.