It’s hard to be theologically precise and not offend people, especially since I’m a rank amatuer at theology.
Some protestants believe that the rift between them and catholics is one of schism. Anglicans who believe in apostolic succession are one sort like this. Catholics don’t believe the word applies because the catholic evaluation of what took place after Hnery VIII was that the Church of England thoroughly rejected the Sacrament of Holy Orders as Christ intended it for more than a whole generation. They eventually reformed their teachings and re-embraced the idea of Holy Orders as a Sacrament, but not until all their valid bishops had died off. You can’t have a true local church (catholic theological definition) unless you have bishops with valid Holy Orders. Unfortunately, the best precise definition for what the protestant reformers did when they broke from Rome and changed certain doctrines is heresy, not schism. I say unfortunately because it’s such an incendiary word. That said, protestants today can’t be described as heretics because they aren’t the ones who established the rift. They inherited it and don’t in good conscience know there is more to ‘church’ than they’ve been taught.
There is a schism between catholics and Eastern Orthodox, another between catholics and the SSPX (which they deny, but it meets the definition). Protestant churches don’t really meet the catholic definition of the word ‘church’. In precise terms they are called protestant ecclesial communities or some other polite term besides church. The individual people generally ARE members of the Church via their baptisms, but their associations at the local level aren’t churches.
It’s complex and confusing stuff. In regards to dissident nuns, it’s one thing to simply be angry about mandatory priestly celibacy. If that were the only issue and they grouped together with a rogue bishop to form their own ‘church’ it could theoretically be just a schism rather than apostasy. But in real life a nun that far down the road of dissent generally also has loose views on sexual morality (fornication, homosexual unions, divorce, etc), utilitarian approaches to the dignity of the human person (abortion, embryonic stem cell research, euthanasia) and so on. When you reach the point of defining bad as good, it really isn’t schism anymore, it’s apostasy.