Yes, FSK is Frequency Shift Keying.
OOK = On Off Keying
ASK = Amplitude Shift Keying
CPCA = Carrier Present Carrier Absent
The latter 3 are more or less the same.
Your remote uses FSK. See...
[Link: gullfoss2.fcc.gov]While it's possible to build a converter, it's not going to be cost effective. FSK receivers and transmitters tend to cost 10-20 times as much as ASK. Offhand, I don't recall seeing any for this frequency.
You would need an ASK 418MHz receiver and an FSK transmitter for 315.625-316.425MHz. If you are lucky, you can learn the codes as IR. If you're unlucky, you'll need to find an FSK receiver to learn the codes.