There are two separate veins of time-travel/causality theories.
A new timeline branches off when one goes back in time (not "going back in time" as much as simply going to a different alternate universe/timeline where conditions are identical to how things were at the target point. See: Dragon Ball Z).
Causality is absolute, and there is a single timeline. any changes made to the past have already occurred, and thus are not "changes". They're simply events on the (immutable) timeline. Once something has been experienced, it is frozen and will always happen.
So how does time travel really work in The Terminator Universe? (I'm talking about the movies, but If someone has information about how it works in SCC it's ok).
For example, in T1, we could say that they follow the second one, but in T2, we learn that the events in T1 did changed the future (first theory) because of the arm and chip of the first Terminator SkyNet technology was improved, BUT then in the same movie, Sarah, John and Uncle Bob destroyed Cyberdyne facility, and nothing happened, the liquid terminator is still there in the timeline, but ultimately they did push back judgement day. So they did changed the future.
Also in T4 John is surprised that SkyNet developed better terminators faster than in the original timeline.
This is also relevant: Why did future John Connor bother to send the T-101 Terminator back?
The most upvoted answer states:
The point is that time travel movies, by their very nature, have plot holes like this related to time-travel paradoxes. We, as the audience, just need to go with the flow, and take such things as a grain of salt.
So is time travel in Terminator inherently inconsistent and we just have to accept that it is the way it is? (My jerk brain is bothering me with this, but he is totally ok with the fact that Cyclops eyes are doors to another dimension)