Baptism
Baptism marks the start of the journey of faith as someone becomes a Christian and joins the family of the Church. Children and adults can be baptised; both make promises about the commitment they are making to follow Christ. Parents and godparents make those promises on behalf of the youngest children.
Thanksgiving
Thanksgiving is a service of saying thank you to God for the gift of a child. It can come before baptism or instead of baptism if you don't yet feel ready to make a full Christian commitment on behalf of your child.
See a brilliant Introduction to Baptism and Christening in the Church of England.