There are four kinds of Roman Catholics

Ultramontane - Believe the Pope is infallible

Ultrajectine - Believe the Pope is not infallible

Sedevacantist - Believe the current Pope recognized by mainstream Catholics is an Anti-Pope and the Papal Chair is vacant

New Catholics - Ultra Montane and not Sedevactantist established in 1870 AD

3 Types of Old Catholics

1 Ultramontane and Sedevacantist

2 Ultrajective and Sedevacantist

3 Ultramontane an Not Sedevacantist

5 Bonus

Self Appointed Popes