Just answering from my POV.
My story is fantasy, which takes place on a fictional version of a real island; the fictional Island is a sort of alternate-dimension "hub" where people from various time periods end up. So while the Island basically exists in the past, it's in a mixed-up, alternate version of the past. This Island is the "shadow" of the real island and exists in the same place, just on a different dimensional plane/time.
Two of the known ways of getting there are by traveling through a very heavy fog when it descends upon the "regular" island--this is how most people end up there, accidentally--or by utilizing some sort of device that allows for travel between various dimensions/time periods. This is not sci-fi, it's just how I as the author try to explain how the fantasy works.
To try to keep it simple, in the fantasy world I created there's a sort of "medicine" which allows for this interdimensional travel and it can be woven into various objects to allow easy passage. The main form of such medicine is called "Weaver medicine" because it's produced by beings known as the Weavers--basically, large spiders who spin webs of this medicine. If pieces of the webs are taken and inserted into, say, the walls of a tunnel, what's an ordinary tunnel can become an interdimensional portal to another time or place. Weavers aren't the only ones who create such medicine but they're the main ones.
Similar medicine is at work in various other magical locations, for example, portals owned by powerful spirit beings. A specific example in the story is a large Tree that has a room with entryways to various lands. Another character creates "shortcuts" by digging tunnels, which are obviously infused with Weaver webs. A third, powerful spirit character lives on a mountain which seems to exist on the same sort of plane as the Island as it travels between dimensions while staying in the same place (i. e., it isn't always "there," yet it is). In cases like this the medicine seems to be associated more with a specific location than an object.
The only thing is that this medicine is unreliable/unpredictable and one can end up in a place or time period different from the one they're seeking. There's
usually a way to get back to where one wants to go, but it involves lots of searching and trial-and-error. The gateways out of the Tree open up into midair a lot of the time and disappear behind the user, to reappear in different places once they're used again...it gets much more involved than this and I'm afraid I can't get into it without getting too confusing. Even in the story, the protagonist is confused, and accuses the Tree of being "broken."
There's also dream travel, but this is only mental, not physical.
My protagonist first reaches the Island of the "past" by taking a ferry boat through the heavy fog. For some reason, the rest of the passengers don't end up there with her. This is probably because the Island in question is sentient and "draws" people to itself, and those who are meant to stay can stay, while those who are not meant to usually can't find their way back to the Island once they've left. A few people can travel freely from the Island to the mainland of their own time, but this is very unusual, so people usually end up "trapped" there. (If they were to try leaving, they might end up in the wrong time.) When my character has to return to her own time, one such person who can easily travel between the time periods/dimensions takes her in his canoe, through the fog, and she ends up back home while he apparently remains in the past. She comes to back on the ferry and assumes it was a dream since nobody else remembers what happened. There's no explanation of what exactly happened when she shifted into her own time while he remained behind; I'm assuming he witnessed her disappearing from his canoe.
In the second story she uses a dreamcatcher which unknowingly has Weaver webs in it; when moonlight hits it its shadow opens a portal which leads to the Island. (The entrance to the portal fades slowly away when the shadow disappears.) She uses this to return home as well. When she uses it to go to the Island in the third story, there's no moonlight, so she uses the light cast by flashes of lightning; as a possible result she ends up in a different location on the Island from the time when she first used it. If/when she uses this device in the fourth story, she's again going to end up in a different spot, indicating that this method of travel isn't terribly reliable.
I realize this doesn't make much sense in the reading, but that might be because this is fantasy and not sci-fi!
But there's lots of overlap of such concepts as time periods, dimensions, and dream/reality. They're all tied together somehow. That's the approach I take to get somebody into a different time period, since I'm horrid with science. It sounds better in the story, anyway.
Not to mention my stories have a heavy emphasis on the power of dreams.
I prefer taking the middle approach, not just the "Bang!--she's in the past" method or a hugely detailed explanation. The reason being, I can't stand it when people just end up in a different place/time period and there's no explanation; it's too much of a convenient device. It's too easy and feels like a cop-out. But on the other hand, if one spends a vast amount of time explaining the method, it can also seem too contrived if the character has to end up in the past quickly. If the writer has to spend a huge amount of time explaining
why this is happening, it kind of draws away from the immediacy of the plot and focuses too much on the how, so the reader will end up thinking that the time travel
is the main focus. Plus there's the risk that the explanation might be too confusing, like mine probably is! (For the record, I certainly don't go indepth trying to explain it all in one spot like I did here!)
I would come up with what sounds like a feasible/sensible method based on the mythology/facts/technology presented in the story, make it as simple as possible but make sure it's not too convenient a device, and use that. It has to be a balance between simple and complicated.
To avoid irritating me personally, I'd just avoid the "Bang!--she's/he's there, don't ask how" method. That's the most irksome thing, IMO. Way too lazy.
I would say that the time travel element, no matter how it's done, would turn the story into "historical fantasy"--some sort of fantasy, at least--but that's just me and I do not know publishing guidelines on such things.
I am pondering over some quantum/metaphysical/subconscious/dream vs reality solution for it; I have absolutely no idea so far.
My approach, personally.
ETA, on reading further posts: I'd be very careful treading into "It was all a dream" territory. Lots of readers feel like this is a cheat when it comes to spending time reading and getting into a story, only to find it "didn't really happen" (even if it really didn't!). They realize that all the personal developments and dangers the character went through were imaginary, and they were never in any sort of trouble, and that's frustrating. If it's all going to be a dream, maybe you should decide that it was a dream, but not JUST a dream? After all, such as in my own stories, dreams are their own realities. And even "just dreams" can have a profound impact on a person's development and point of view.
I. e., don't have it be just a dream, have it be a dream with a purpose. (Besides just entertaining/educating the reader.)
No way do I want to open the can of worms of trying to define the difference in general.)
