[caractacus]

I think it depends on the show in anime. SPOILERS FOLLOW. Erased is not a parallel world, but someone trying to change their past. Madoka finds Homura repeatedly doing whatever is possible to save Madoka. Steins:Gate is timelines and parallel worlds (think of how many times Okabe again and again tries to save Mayuri). Girl who Leapt Through Time is the Groundhog Day story, same day over and again; bit like Tatami Galaxy. No idea where something like Haruhi Suzumiya might fall where time is played with in many different ways.

Meanwhile Evangelion (the later films) and Attack on Titan both seem to be veering towards some kind of inability to stop the same grand narrative cycle repeating again and again...

[Izkata]

It also depends on the show in American media. Star Trek, for example, has nearly every version of time travel at some point or another - except the "simultaneous worlds" version described in GP with Back to the Future and Timeless.