Hi Jason,
As always... every regional is different. But yes... some do have "training contracts".
The fact is... when an airline hires you, they invest tens of thousands of dollars in you during your initial training. Ground school, hotel, per-diem, travel, FTD's, Full motion SIM's, and IOE (Initial Operating Experience).
So, some of the airlines want a promise from you that you won't leave in a few short months since they consider you an investment. Thus... the idea of a training contract. Some may say that you have to pay back "training costs" if you leave before "X" date. While other's may have pro-rated pay back schedule based on a timetable they set up.
Personally... I'm not a big fan of "training contracts". Typically you'll see them offered from some smaller airlines or even some without a strong organized pilot group, and maybe even some from some airlines that are less desireable to work for due to poor contract rules, pay, pilot retention/turnover, etc.
Either way... you have to weigh your personal and professional options when it comes time to apply for a professional pilot position with a 121 carrier. As you can plainly see... not all airlines are created equal.
Researching each airlines work rules, contract, pay structure, etc... is a great place to start. It seems you are already on a good path of research. Keep it up!
Bob