There are other theoretical types of paradox in conversations about time travel, though most are about how "real" time travel would affect the world.

For example, the Fermi Paradox - "where is everyone?". The idea is that, if time travel will ever be possible, travellers should already have started coming back way in the past already and any character or person learning about it for the first time should probably take it for granted.

Another, arguably a Grandfather Paradox variation, is the Hitler Paradox. Say for example I headed back in time to prevent something happening, did it successfully, and headed home. This is a paradox, because now there's no way I could have known about the event I just prevented in order to prevent it. There was no reason for the time travel to happen at all and the future I go back to shouldn't be the same as the one that sent me. So how did they send me, and will there be another me when I get back?

The Grandfather Paradox is specifically about the traveller's own existence. They have prevented themselves existing to prevent their own existence.

Skynet's situation is sort of another Bootstrap Loop, it seeds itself in the past just as John ensures his own conception, by steering Kyle towards it.