Does Catholicism teach the the Catholic Church is one groups of people out of many that are members of Christ's Church?
Iowans are one group of many that are Americans.
In a sense yes, but, that those outside the Church are in error. This doesnt deny your Christianity, it just says yer' 'doin it wrong.
And to head off the inevitable " no salvation outside the Church" citation I believe will make it's appearance in one of your future posts I will direct you a very simple explanation on the subject here