The premise of time travel movies is a person being able to be present at a different time to their original timeline. So I guess you could say a Groundhog Day type of movie is a subgenre of the time travel genre.

Edge of Tomorrow.

Plot - Earth is invaded by aliens. Tom Cruise gets a power where if he dies, the day starts over. So, he keeps pushing forward in the warzone, and if he dies, he knows how he'll get attacked and adapts to it.

I think it depends on the method for the loop, and how time itself plays into the plot.

Like, I wouldn't say Groundhog's Day is a time travel story. But Deathloop (the game) is a time travel story. The main reason for this is that Deathloop explicitly tells you that the loop is caused by a time machine device, where as Groundhog's Day could be interpreted as Bill Murray having died and is now in Hell or Limbo.

The way you escape the loop in Deathloop is to get all the looping people to die and then destroy the machine. In Murray's situation in Groundhog's Day, the solution is to... Be a better person?

Here's a list of films featuring time loops.

I say no.

Time travel stories are about going to a different time.
Time loop stories are repeating the same time.
It's really that simple.

Time loops are anti-time travel really, as there's no movement in time at all.

I think we have to consider it different. In Back to the Future and Looper, one could travel to a past where another version of oneself exists. In Groundhog Day and edge of Tomorrow, the character travels back to become that version of his self again and again. The character can remember and learn, but isn't cloning himself.

I say yes. It's one of my favorite genres (if you can call it one) and definitely includes loop-based plots like Groundhog Day and Primer. But I also enjoy the Terminator Series and Back to the Future and others that don't really loop that way. I suspect most fans are similar. It's hard to imagine enjoying one premise but not the other.

Also: https://xkcd.com/657/

Well, when the loop takes place there is a travel in time taking place… but not as in the standard time travel films.

I think is important to point out that in the Groundhog time loops the travel is only of the memories or the information, there is no energy-mass traveling (though information is a kind of energy, let me skip physics here), and the traveler at the beginning of the loop has not carried anything from the future but the memories of the previous loop, did not age or suffered physical modifications (there may be exceptions, sure).

So I think that is a kind of time travel, but a sub-genre where the travel is less material than in the typical time travels.

Infinite Isekai

Here’s one: where do you put things like The Long Earth where it’s not time you step through per-se, but all the possible futures starting from the beginning of the universe?

I really want to see someone make that series into a movie.

Netflix categorizes them that way...

I mean, time-travel stories typically involve traveling by way of some mechanism be it a spell, wormhole, tear in spacetime and etc. The end goal is usually traveling from one point to another with a purpose. Characters can travel back and forth. Everyone usually remembers each encounter.

Time-loops, like in Groundhog's Day or Edge of Tomorrow, usually cause people to get "stuck." Some plot device is then introduced to eventually "unstick" them. Only the people stuck in the loop are usually aware that anything is happening.

The question is whether a time loop is a form of time travel.

Are they actually going back in time? Or is time itself looping back on itself? These aren't the same cause, though the effects can look the same

So I suppose, conventionally, it can be thought of as a subform of time travel. But from a technical perspective, it may or may not be

Naked (2017)

Plot - Rob is caught in a time loop as he keeps waking up naked in a hotel elevator on the day of his wedding. This is a remake of the 2000 Swedish film Naken.

Not a great film, though.