According to the FCC's interpretation of the TCPA, auto-dialers have a minimum of two components:
1. Something with the capacity to generate and/or store telephone numbers, and
2. Something that dials those numbers.
The first can easily be any computer database, whether the person has it on their office computer or they're using an online service for it. If it stores and communicates the numbers to the dialing mechanism, it qualifies.
The second is anything that actually dials those numbers; flacorps basically covered it. Whether it's a piece of hardware that receives the numbers from the database and dials it over an office line, or a piece of software that uses a modem, or even a 3rd party service/software that connects an agent with the dialed number.
I believe those are the only two required components. A physical phone would even be optional. The agent could have a USB headset plugged into their computer and it be completely done over VOIP.
This is an article on two cases involving the FCC's opinion with different outcomes. The main points may not directly relate to all of the "components", but it beats around the bush and the cited cases may have more insight: http://www.law360.com/articles/518599/confusion-over-fcc-s-autodialer-definition-continues