There is no difference between a christening service and a baptism service. Some churches use the word 'baptism' and some the word 'christening'. Babies are 'baptised' during a 'christening' service just as couples are 'married' during a wedding service.
Christening is a traditional English word which means to become a member of the Christian church. Baptism means to be immersed in water. During a christening service a baby or child will be baptised with water and welcomed into the community of the local church