you are baptised, In the name of the Father, the Son, and the Holy Ghost in the Catholic Church....you are not Baptised in to the Church...as you stated...it takes a couple of other sacraments to make one a full fledged Catholic, like Confession, Holy Communion, and Confirmation...which is at the age of around 13 and is an acceptance of Jesus Christ as the Son of God and Savior....similar to the water Baptism of Baptists at around that age....Here is the difference:
In mainstream Christianity, a person accepts Jesus and is Baptised when they have an understanding of their actions.
In the Catholic Church, an infant is Baptised INTO the church. There is NO accepting of Jesus involved. So the person grows up and lived without ever accepting Jesus, but they think they are a christian.
Water baptism is done at birth, accepting Christ as Savior or in Spirit and Faith is done at around 13, through confirmation....
unless ye is born again of water and the Spirit...is what he told Nicodemus I believe....
The Catholic tradition does NOT conflict with the Bible in this manner....
care