If I can transfer a fire, can I light a new fire on yom tov? What's the difference between lighting a new fire and transferring a fire? Aren't they part of the same melacha?? The melacha is to create a fire or burn something!
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The Torah says "what is consumed by all people" is work that can be done on yomtov.
The Biblical prohibition on "burning" is in fact not in force on yomtov (i.e. "no-work" holidays other than Yom Kippur, when not on Saturday), provided it's for the right cause (more below). But creating a new fire is a separate problem of "generating", which is a rabbinic prohibition. (It does help remind you that it's still not a usual work day.) But you are correct that on Shabbos or Yom Kippur, it would be the same Biblical prohibition of "burning" whether you strike a match or touch an existing flame to a candle.
On yomtov, it is permissible to transfer an existing flame to cook food (to be consumed on that specific day of yomtov, by Jews), warm up a room (e.g. fireplace), light a candle, or use hot water to wash your hands and face as those are all considered "appreciated by all people." Not very long ago, smoking tobacco products had been seen as "universally appreciated" by the folks who brought you the Marlboro Man, but most of today's rabbis aren't buying it. Using hot water to shower your whole body hadn't been seen as "universally apppreciated" in medieval France, but many rabbis are reconsidering. (Now Ramban felt there was a specific rabbinic prohibition on showering ... but that's beyond the scope of this question.)
That's a quick overview. If you have more-specific questions, please ask them separately.
See Mishna in tractate Beitza page 33a: "One may not bring forth fire from wood, stones, earth, tiles nor water etc."
Shulchan Aruch Harav ch. 502:1 explains the reasoning, since creating fire is considered "Nolad" (creating something new) versus lighting from a pre-existing flame which does not bring forth something new into this world (which is forbidden on Yom Tov).
The Rambam (Shevisas Yom Tov 4:1) writes that the reason one may not kindle a new flame on Yom Tov is because one could just as easily do it beforehand.
We find a similar idea with various Yom Tov related rabbinic prohibitions, such as cutting hair on chol hamoed, which one may not do because one could just as easily do it beforehand, and allowing people to wait may potentially cause a lack of honor to the holiday (Moed Katan 14a; Rambam ibid 7:17).