I probably need to clarify this. Baptism is a sacrament that involves water touching the baptizee and is done with a Trinitarian formula on either an adult who wishes to become Christian or an infant whose sponsors wish him to become Christian. It remits the original sin but (unlike the baptist belief) does not confer ultimate salvation. The baptizee, in all probability will sin and whether or not he is justified at the end of his life remains an open question. The Orthodox may wish to modify my statement regarding remission of original sin; our differences here are not material in discussing church membership issues.
Confirmation is a sacrament that prepares one to begin receiving communion. It is done differently in the West and in the East. It does not confer membership in the Church (baptism does that). It advances one on his road to holiness, just like the Baptism that preceded it and the Eucharists that follow do, but it does not make one "saved" forever.
There is no sacrament of the Church that bestows the status of accomplished salvation on a living person.
The Catholic Church recognizes baptism when performed by a lay person, as long as water us used in the name of the Father, the son, and the Holy Ghost. In an emergency, valid baptism can be performed by a non-Christian. Certainly, baptisms done in a baptist church are valid. However, baptism is valid when it is validly performed, not when, if at all, a conversion of the heart happens. If Jake, 20 years of age, experiences a conversion to Christ, and is baptized in a baptist church, he is baptised when the baptismal prayer is said and the water touches his forehead. A baptist would say that Jake is baptized at the time of the conversion, while the water and the prayer are outward symbols. So, we agree that Jake ends up a Christian, but we disagree on the exact mechanism of becoming a Christian.
"It remits the original sin but (unlike the baptist belief) does not confer ultimate salvation."
"A baptist would say that Jake is baptized at the time of the conversion, while the water and the prayer are outward symbols"
A Baptist would say that a person is saved (born again) at the moment he/she trusts Christ for salvation. The ordinance of Baptism can be carried out at any time after that and has nothing to do with the believer's salvation except as an outward witness of what has already taken place, i.e. the identification of the person with the death, burial and resurrection of Jesus. It confers no saving grace, nor washing away of any sin; it is a symbol of an inner change.