Zoro's Ashura is just an illusion caused by very fast movements.
Sanji's Jambe was caused by friction before the time-skip, but during the time-skip he became able to create fire just with passion.
Why exactly Sanji is able to create fire with passion is a more complicated matter though. And I'm hoping it's because Sora is a descendent of Lunarian, as others have theorized, and Judge didn't know it, so Sanji was able to keep at least part of the Lunarian powers precisely because Sora prevented the Germa's genetic manipulation from working on Sanji's body, which would have removed the Lunarian powers from his body.
Too bad I can see a problem in this theory, which is that Sanji's awakening gave him powers too similar to the ones of his brothers, so it's hard to think of an excuse that Oda could use to make it so that Sanji was really able to escape from the genetic manipulation.