Beware of people who try to confuse you by saying that there is a difference when there is none. There are people who have their own reasons for wanting to confuse others about the meaning of these plain ordinary English words. If you have been Christened you have been Baptized. People can still debate who should be baptized, and whether we should baptise young children, and there are differences of opinion about that in good conscience which we should respect, but to say that someone has 'only' been Christened is nonsense. Whether it is right or wrong that they should have been baptized, no matter what their age, they cannot be Christened without being baptized, for that is what Christening means.
People are Christened by being brought into Christian fellowship through baptism.
So baptism is the rite of Christian initiation. It marks the beginning of a life of belonging to Christ. It has no other meaning. If a person is not related to Christ, so that he or she, however old or young, is not learning the way of Christ and being renewed in that relationship, then there is no point in saying that person is a Christian. It is a gift of God Firstly, we are related to Christ, and to God through him, because he took the initiative and reached out to us.