I don't know of any christian faith that says they they do. It seems to be a fairly recent popular misconception, often used by those unfamiliar with christian theology to mock it.
Angels are supposed to be an entirely different order of beings (or several different orders of very different types of beings), and are usually considered higher than humans currently are but lower than what we can become. Essentially, they are God's slaves while we are his children.
On the other hand, Jewish tradition sometimes claim that Enoch and Elijah (who were taken to heaven directly, without death) became the archangels Metatron and Sandalphon.
The biblical references to Lucifer actually refer to the kind of Babylon, not Satan, although they could perhaps be extended to satan typographically.
I think what you are thinking of is the the Islamic view of Satan. In that view, Satan was the greatest of the Djinni (which are of a similar status as angels but are made of incorruptible smokeless flames instead of pure light and which have free will like humans instead of the perfect obedience of Angels) and he loved God more than anyone. God had first commanded his creation to worship no one but him, but then he ordered the angels and Djinni to bow down to and serve Man, which was made from clay but bore the image of Allah. Satan could not see the image of god in these lesser beings and chose to adhere strongly to the earlier commandment and serve no one but God. Of course, by disobeying the later commandment he was also not serving God, which caused all sorts of problems. Pride was part of the sin too, as he considered humans to be inferior to him and did not like them being treated as greater.
Iirc, in the Islamic view all individuals also have a Djinn associated with them and having the same appearance, sort of like a guardian angel or a Roman Genius/Juno. While the soul leaves this world, the Djinn remains and may be seen as ghosts. There are some references in the bible indicating that a similar view (but in which djinni were called angels) was common among Jews at the time of Christ and that the disciples themselves may have believed in it. If I recall, the first people to see Jesus after his resurrection thought they were only seeing "his angel," but I might be confusing this with a time that thought one of the disciples had died. There isn't anything indicating that this view should be considered correct though.
