The sedes reject the pope because he acted in heresy (as they see it). The danger of vanity is that we can say no one has the right to judge the pope.
The R&R's reject the pope because they feel he rules in error or approaches heresy (as they see it). The danger of vanity is that no one has the right to judge the pope and that goes for nitpicking his every little action to determine whether or not it's valid or at least valid enough for the R&R types.
How are they different? Both groups judge the Pope.
How are they the same? Both groups are adhering to the Catholic Faith to their best of their abilities.
They both refuse to follow his errors, ambiguities and heresies and for that I applaud both camps.
Who can disagree with them? I say over and over again that the post-Vatican II popes are not to be followed because that would be following indifferentism or outright denial of Our Lord. When someone says they are respecters of other religions, then they are saying they respect a person who denies Our Lord and that they respect a religion that empirils an eternal soul. Well, Our Lord said that those who do not believe are condemned already and that the gods of the gentils are devil's and that's good to follow.
Really it can all be distilled to "Do Not Follow Them".
And this advice applies only to this period of conciliar heresy (1962 - present).
The difference lies in this:
One deposes the Pope without authority to do so (despite erroneoue interpretations of Can 188.4);
The other waits for the Church to depose him, should it decide to do so.
So far as I am aware, the only way a pope could be deposed for manifest heresy without a judgment from the Church -via Can. 188.4- would be for the Pope to make an admission of heresy.
And so far as I am aware, he has not made such an admission.