The T:TSCC version of time travel was essentially that the act of going back in time and changing anything created a new timeline, but did not destroy the old one. Essentially, time line A has a guy go back to 3/20/2013 and assassinate a person who will grow up to become an infamous terrorist. A new time line (time line B) is then created from that moment and essentially from the point of the change, the timeline skips the original time line A that would have happened after that change and goes to this new time line B. Think train tracks switching...the train track before the switch is the same, but after the switch you get placed on a new track. The other track that you normally would have been able to travel on isn't destroyed, but you can no longer access it after the point of the change. Essentially, this creates an almost infinite amount of possible time lines, but only the time travel/people who are on that time line will experience the change. This is also why things like a grandfather paradox would not apply or any other changes that would normally impact the time traveler themselves.
Now Continuum has shown that older Alec has memories of all the stuff going on during the show and sends everyone back as part of a plan. This normally creates a paradox: Alec creates a time machine to send people back in time, because when he was younger he met people that his older self had sent back in time, thus he knows that when he gets older, he will have to do this. Now they could potentially use the T:TSCC model, but this implies that someone already sent (at bare minimum) Kira back in time previously, which inspired older Alec to hatch this plan. Terminator sort of has the same "what is the origin time travel?" issue, where we never truly know what "time line zero" was. For all we know, the time line currently being experienced is the culmination of hundreds of previous time line alterations.
