2 of him... Except it's the same one...
This is a theory, or more just speculation based on some amount of evidence and some amount of guessing.
A little while ago, I had the thought of "Haha I wonder if there's two Gaster's hanging around in Deltarune since there's the one visiting from Undertale and maybe there's a Deltarune version of him like there are for many other Undertale characters". I thought that was a fun idea, but then recently realized NO, ... It's even better.
Consider Gaster and the skeleton brothers. We don't have hard solid proof that they were family or knew each other, but it makes sense as an assumption based on the font naming scheme (Wingdin{g aster}), and the vague appearance of Mysteryman (Not confirmed 100% to be Gaster but makes sense as an assumption and is at least connected), and Sans and Gaster both having involvement with the True Lab, meaning Gaster is probably a skeleton too. We're going with that assumption for this post at least.
Next, consider the possibility that Papyrus and Sans are originally from Deltarune. Again, this isn't a 100% thing but does have evidence for it. Sans and Papyrus are said to have 'Just shown up one day and asserted themselves', all Sans' lost soul dialogue about not being able to 'go back' or 'see them again', Riverperson saying "Beware the man from another world", Deltarune Sans and Papyrus making sense as a Sans and Papyrus with earlier character development (Papyrus not having any friends in Deltarune leads to him wanting to be popular in Undertale and make friends). This idea could end up not being true, but we will also be going with this assumption for this post.
So, if Papyrus and Sans, and Gaster, knew each other or were family, would it not make sense that they migrated from Deltarune to Undertale together.
And right now in the red soul and Kris' adventures in Deltarune, Sans and Papyrus are still there. They haven't made their trip to the time and place they appear in Snowdin in Undertale. So, if we were to assume they all make the trip together, that would mean that Gaster at a previous point in his character development relative to how we know him is also around still in Deltarune somewhere.
This is also working with the assumption that I also feel is safe of the Gaster and Chara we hear in the opening of Chapter 1 and in the UI for the save file menu are visiting/on a mission from Undertale. I don't see any reason for an endemic Gaster and Chara, if you will, to be doing what they are in Deltarune. It seems to be a mission with Chara wanting to achieve a better ending for their family in Undertale, and Gaster has... Whatever motives he has.
Brief aside in this post, but I also think that Frisk is there too as the red soul to have continuity with who the red soul in Undertale is. I don't know if Asriel is there anywhere, but I do think Frisk and Chara are still a team and are cooperating with Gaster in some way. I'm not sure how apparent it was to other people, but to me there was a very clear and startling difference in the narration styles between Chapter 1 and Chapter 2 of Deltarune. With Chapter 1 it was like "Hm, if this is Chara they seem kind of, down maybe? Not even pulling their whole 'Ah wow woah it's a 'hole'' schtick, not quite as many jokes, different speech patterns.", and then as soon as narration started in Chapter 2 it was like "Oh. This Is Chara." The mannerisms of speech and tone are just completely back to the way they were in Undertale. So if I had to guess I would think that maybe Frisk narrated in Chapter 1 and Chara narrated in Chapter 2? They could be taking turns. I just wanted to explain that as part of this post because it fits into the whole "Characters jumping around between worlds" deal going on.
With all that out of the way though, I'd like to present my highly detailed diagram depicting the mess I've been talking about:
[Image ID: A simple diagram made out of colour coded lines. A yellow and purple line running parallel in the same direction represent Undertale and Deltarune, respectfully. A turquoise line representing Papyrus, Sans and Gaster runs along the Deltarune line before swerving backwards and into the Undertale line. Later on along the turquoise line on the Undertale side, a grey line representing Gaster, and a red line representing Chara, and probably Frisk as well, swerve off the Undertale track and backwards towards the Deltarune one, so that the turquoise and the grey and red lines cross each other in an X shape in the middle. End ID]
And there you have it, this is what the time and place travel looks like it's shaping up to be to me, but of course I am always eager to be proven wrong and surprised with this stuff. I'm looking forward to looking back on this later and seeing how right or how wrong I was...
Hopefully this was interesting or fun to read! There are so many questions in these games and so much to think about, and I love seeing what everyone else is thinking about it too! One other post I remembered is this one [link] from @undertale-encyclopedia that explores the idea of Gaster, Mysterman, the Man, and Him, and what the distinctions could mean, if there are more than one entities of 'Gaster' in whatever way. It's very smart and from a great blog so definitely read that one too if you liked this one!
Anyways, that's all from me... See you later, Fellow Fans...!
{Errata (That's not all from me); Gaster is present in Undertale a good ways in the past, far enough to be the royal scientist before Alphys and design a bunch of things, while Papyrus and Sans arriving in Snowdin is talked about as if it was relatively recent, given that it's notable information to one of the monsters in town. This makes the assumption that they travelled between worlds together shaky. The narration in Chapter 1 and Chapter 2 share the same 'It's a locker' jokes, maybe suggesting that the narrator is the same between them after all. (Or they just find the same jokes funny.)}
