There is a lot of conflicting speculation about the origins of the Titans, not least because the stories themselves were understood differently by different people in antiquity, and the details varied from region to region within the Greek world.

Some people want to see a naturalistic or euhemeristic explanation; others want to see them simply as entertaining stories. The most plausible explanation, in my view, and the one that best fits the ancient texts as we have them, is the cosmological one. That is to say, the titans (children of Ouranos and Ge) represent primordial measures of time; a kind of 'deep' cosmological order that is superseded by the anthropocentric Olympian gods.

Homer and Hesiod both characterise the Titans as gods of Tartaros which is opposite to Heaven, - that is to say, the 'underside' of the Earth (the invisible stars), as opposed to the hemisphere of the visible stars, where the Olympian gods reside.

It's widely accepted that elements of Greek cosmology were adopted and/or synchretised from Near Eastern religions, in addition to whatever common Indo-European roots Greek religion shared with neighbouring cultures. But as to whether the titanomachy represents a separate pantheon of gods assimilated into Greek religion for political reasons, there's no evidence... So: we'd need to establish first of all a.) who these conquered people were, and b.) that they did in fact worship deities similar to the Titans, preferably with the same (or similar) names. As it stands, the names of the Titans fit very well with the cosmological interpretation of the Greek myth as we know it, so it seems a bit inefficient (vis-a-vis Occam's razor) to postulate additional, political or acculturative explanations.

[Edits: added more detail, 'cause the first half of my post didn't really get to your question.]

P.S. Also, found this earlier thread that asks your same question, and has some good discussion.

In Norse mythology, the giants are explicitly not gods and the Vanir are; in Skáldskaparmál, the Vanir and Aesir have a war and make peace by creating a human, and in Ynglinga Saga, there's a lot more detail about who fought who and how they got over it (and it also has one of my favorite scenes, with Honir, the god of indecision, hemming and hawing his way through negotiations until his advisor is beheaded).

Anyway, Vanir are gods, ruling mysteries of existence, creating new life, all that jazz.

The jotnar are more linked to natural phenomena, like the ocean and mountains, and seem to be related to something more like genii loci, or spirits of specific places. God-like, and literally related to gods (or at least Aesir) but not quite divinities. Thurs are enemies of the Aesir, but also seem to be elemental in some ways, embodying fire or ice (here's a paper that cites some sources on that - a pdf) but without much consciousness.

The giant Logi, for instance, is fire, who wins an eating contest by consuming everything. Jord is the name of Thor's mom, but also a word that means "land".

I think I've read something about Vanir maybe being older gods, but it was something kind of old and sort of speculative. Giants seem to be a different order of being.

Edit to add: Almost certainly, I'm thinking of something about Hulda/Frau Holle, maybe even written by Jacob Grimm... although she's related to Jord, not one of the Vanir. Hmm.