The Devil

Satan or The Devil was the (usually horned) personification of evil in human mythology and religion.

Origins of the Myths
Several beings and groups were a possible source for the idea of Satan.

The Dæmons, a horned race from the planet Dæmos, were believed by the Third Doctor to be the inspiration for Satan based on their experiments on humanity. (DW: The Dæmons) Likewise, the Demoniacs were another species believed to have influenced human society. (BNA: Mean Streets)

The Greek Immortal Hades, a supposed lord of the underworld, was also known to call himself Satan. (PDA: Deadly Reunion)

The Fourth Doctor believed that Sutekh had called himself several names, including Satan. (DW: Pyramids of Mars)

The Beast said that he was the origin of Satan, and all similar entities on all worlds. The Tenth Doctor found the Beast, in particular his claim to have existed before the universe, a challenge to his own belief system. (DW: The Impossible Planet/The Satan Pit) He did eventually refer to The Beast as "the devil". (DW : Planet of the Ood)

Mistaken Identity
On other occasions, entities were mistaken for Satan accidentally.

When Momus stole Joan of Arc from Earth, she believed it was a trick of the Devil. (WC: The Lonely Computer)

In 1140, the Krillitane in Worcester were thought to be the Devil. (NSA: The Krillitane Storm)

In 1928, when Angelo Colasanto learned of Jack Harkness' immortality, he thought he was the Devil. He was captured and killed repeatedly, though some thought he was a miracle instead of the Devil. (TW: Immortal Sins)

When Fitzroy contacted Bryn Williams and tried to make a deal with him, Bryn assumed it was the Devil. (BBCR: The Devil and Miss Carew)