Is a premature baby's vaccine schedule different than a full-term baby's?

Nope. Current recommendations follow the same schedule.
No. As of now the vaccine schedule remains the same regardless of prematurity. It relies on the chronological age of the infant. There is also an additional vaccine that some babies will receive for protection against RSV (respiratory syncytial virus) if they qualify.
Immunization. As long as the preterm baby is well & stable without any problems, immunization schedule is the same as the the full term infant. I hope that answers your question. Good luck.