First this: 818 All who have been justified by faith in Baptism are incorporated into Christ; they therefore have a right to be called Christians
You said: "Catholicism believes that all who believe in Christ, that He is risen from the dead and the Son of God, are Christians"
In fact: There are people who believe in Christ, that He is risen from the dead and the Son of God, but don't believe in baptism and don't believe in the Trinity, and have not been justified, or hadn't you considered that.
Like I said, there are some who believe in Christ, that He is risen from the dead and the Son of God, but are still not Christians.
That's one example. Do you need more?
1257 ...Baptism is necessary for salvation for those to whom the Gospel has been proclaimed and who have had the possibility of asking for this sacrament.... God has bound salvation to the sacrament of Baptism, but he himself is not bound by his sacraments.
1260 Every man who is ignorant of the Gospel of Christ and of his Church, but seeks the truth and does the will of God in accordance with his understanding of it, can be saved. It may be supposed that such persons would have desired Baptism explicitly if they had known its necessity.
836 All men are called to this catholic unity of the People of God and to it, in different ways, belong or are ordered: the Catholic faithful, others who believe in Christ, and finally all mankind....
838 The Church knows that she is joined in many ways to the baptized who are honored by the name of Christian, but do not profess the Catholic faith in its entirety or have not preserved unity or communion under the successor of Peter. Those who believe in Christ and have been properly baptized are put in a certain, although imperfect, communion with the Catholic Church.