If I have connecting flights on two different airlines, do I have to check in on each one separately?

The answer to this will depend on whether or not these two terminals for different airlines are connected directly via an interior hallway (e.g., Albany (NY) International Airport) or if you will need to exit the one terminal and enter the other because there is no connecting hallway (such as at Los Angeles International or John F Kennedy International Airport). If there is a hallway that connects the terminals, you won't have to pass out of one and pass into the other. However, if they don't you'll be forced to pass out of one and into the other, through the Security checkpoint. Check with staff there, if you are unsure to see if they have other methods for getting there.