Yes, but in the US you have Catholics and all the various sects that fractured from the Catholic church, i.e. Christians who don’t follow the pope. They all follow Christianity, which makes them all Christians, but whether they focus on Jesus Christ and the New Testament or focus on god and the Old Testament is where the distinction lies.
The way I have always viewed Christians vs Catholics is that Christians fundamentally believe faith in god is the only requirement. In Catholicism it is not enough to believe, but they believe that good deads are required, hence Catholic guilt. In that way, Christians don’t really care about the new testament and the teachings of jesus, believe in god is all they require to be good Christians.
Correct, again its just been my experience that non-catholic Christians will generally refer to themselves as Christians and Catholics will call themselves Catholics over saying they are Christian, at least in the US.