A predestination paradox occurs when a time traveler is caught in a loop of events that "predestines" or "predates" them to traveling back in time. To simplify, this means that the person does land in the same timeline that they started off from, but anything that (s)he does will only create history as (s)he knows it. Let's assume John is someone who lost his wife to a car accident. Years later, John finds a way to travel back in time and decides to save his family. Once he goes to the past, he enters a car and rushes to the location where his wife met with the accident... only to crash into her car and kill her. An event of the future predestined an event in the past. The timeline is immutable. This type of a time-loop also gives birth to another sub-paradox...

The Bootstrap Paradox

The above time-loop can give birth to something present neither before nor after the loop. Let's assume Jess and Jane are good friends. One day Jane gives Jess a pen and says, "keep this safe and give it to me after one year". Jess does so and hands the pen over to Jane after a year. Jane then stumbles upon a time machine and travels back to the past by one year. She carefully avoids her younger self and meets Jess. Jane gives Jess a pen and says, "keep this safe and give it to me in one year". In this loopy nature of things, the pen was bootstrapped into existence for that 1 year, seemingly from nowhere.

The most prominent example of a film that operates in a singular time-loop has got to be Predestination. The film can really put your mind in a knot. Other famous ones are 12 Monkeys, Interstellar, and, more recently, Arrival. Even the first two parts of The Terminator are constructed in this manner. I could tell you what gets bootstrapped in these films, but that would give away the plot.

Non-Paradoxical - Alternate Timelines