Understand VoIP

I am trying to understand the differences between the great many voip vendors. We are looking for a complete in-house solution. For instance I see the terms IP, IP PBX, Hybrid PBX, etc... In an effort to explain my confusion; I understand (I think) that Cisco has a true IP only solution, while Avaya does not and runs on top of a more traditional PBX system. I have been charged with finding a list of vendors that offer a pure/true ip telephony solution. Can anyone help me to understand the differences if any of IP, IP PBX, Hybrid, etc...? In my reading/searching I have not been able to find a clear explanation. This would help me tremendously to create my list of vendors. Thank You!