[Larry Watts] “Many of the sites where I have found some of these products look similar and I wonder if it is the same program marketed under different names.”
They are usually using open source ffmpeg encoder rather than licensed encoders. The result could be compatibility issues. If you are a professional, avoid them.
With codecs like x264, it can be both open and licensed so the free Handbrake would be fine for that.
With H.264 there are various encoders such as MainConcept and Apple amongst others but they are comply with the official MPEG spec.
[Larry Watts] “I think FCPX uses compressor when it ingests media and transcodes.”
Although it might be more accurate to say they both are using AVFoundation CoreMedia. This is part of the OS basically.
[Larry Watts] “I may bite the bullet and get sorenson squeeze to be certain I’m giving my client the best possible product.”
I’m biased but I like Telestream Episode.