Two Meanings Of "Time Travel"

The term "time travel" applies to two completely different fictional phenomena.

(i) HG Wells' Time Traveller is said to "travel" on his Time Machine to 802,701 AD, then to "The Further Vision," before returning to 1895. In my opinion, what the Time Traveller undergoes is not a kind of travelling but stationary time dilation. However, the term, "travel," suffices for the purpose of differentiating this process from phenomenon (ii) below.

Comparable to the Time Traveller, and still within phenomenon (i), are two of Poul Anderson's characters:

Martin Saunders "travels" in his time projector through an even further future and back around the, in this case, circular timeline to 1973;

Jack Havig, a mutant not needing a temporal vehicle, "travels" through past history and future history and remains in the future.

All three characters have what seems to them to be the experience of "moving" through objective time in a smaller amount of subjective time.

(ii) In Anderson's "Delenda Est," Neldorian time criminals generate a timeline in which Carthage, not Rome, won the Second Punic War. Do the Neldorians even travel back through the familiar timeline in order to do this? Like every other time traveller in their timeline, they do not "travel" between moments in time but simply disappear from one set of spatiotemporal coordinates and (re)appear at another set. Do they appear in the familiar timeline, then disappear from it at the moment when they change history or just not appear in it in the first place? Does the Time Patrol have records of time travellers appearing/arriving in the past, then disappearing, indicating that they have generated a divergent timeline? In any case, this is a very different process from (i).