Bipap is the Respironics name for their bilevel machine. And from what I understand, only a certain type of bilevel machine is gnerally prescribed specifically for predominantly central sleep apnea.
You might have a high pressure requirement, and that can mean a need for a significant level of exhale relief that a bilevel machine can provide. You might have additional respiratory issues for which a bilevel can help. I have weak lungs (although I think there's a technical term for it), plus I have a high pressure requirement (18), and I use a bipap. Exhale relief can also be provided with regular cpaps, with something called cflex in Respironics machines and EPR in Resmed machines, providing a level of measured exhale relief, but a bilevel can provide greater exhale relief. The need for a bipap or bilevel is determined during your sleep study, typically.
And as was mentioned, the type of mask you is independent of the machine. Usually during the sleep study they can tell if you are a mouth breather or not. If you are a mouth breather, usually that is handled with the use of a type of full face mask (covers nose and mouth) instead of the nasal mask (covers just the nose). There are some variations. But masks are like shoes, the fit and suitability largely rests with the wearer. Someone who is male with a beard might have problems with a full face mask. Someone with high pressures might have difficulty using nasal pillows. This is why it's good to work with a good DME that can help with your choice, and most importantly, the fit.