In the Methodist Church baptism as an infant would normally be followed by confirmation and reception into membership at the point where the person wishes to take on the commitment and responsibility of Christian discipleship for themselves and to play a full part in the life of the Church.
This is best summed up in the Methodist Worship Book:
“In Confirmation, those who have been baptised declare their faith in Christ and are Strengthened by the Holy Spirit for continuing discipleship. Confirmation reminds us that we are baptized and that God continues to be at work in our lives: we respond by affirming that we belong to Christ and to the whole People of God. At a Service of Confirmation, baptised Christians are also received into membership of the Methodist Church and take their place as such in a local congregation.”
There is no obvious difference in understanding, for example, between the Methodist Church and the Church of England about Confirmation itself. However, the Church of England does not have any strong sense of “membership” of the Church of England (so, for example, there is no transfer of membership when a person moves from one area to another).