Lilith was originally a storm demon known as "Lilitu" in ancient Mesopotamian myth around 3000 BC and she was thought to have been the cause of disease, illness, and death. She later appears as a nocturnal demon in Jewish lore and the queen of demons.
Lilith was the first wife of Adam, however she was cast out of the Garden of Eden for her sinful ways. After the leave, she encountered the angel known as Samael, who lusted for her and she did to him when he treated her as both equal and superior despite his status. And from their union she birthed many demonic beings. God sent three angels to take Lilith back to Eden, and when the angels found her in the Red Sea they threatened her with the loss of 100 of her demon children every day unless she returned to Adam.
She refused and was punished with having all of her children slain. Lilith took revenge by launching a reign of terror against women in childbirth, newborn infants, particularly males, and men who slept alone. She was forced, however, to swear to the three angels that whenever she saw their names or images on an amulet, she would leave infants and mothers alone.
Lilith later bore the Lilim who would later become the Succubi. And soon after, she became the first and possibly only Queen of Demons as well as the queen of the Inferno itself. She procreate demonic offspring endlessly. Lilith was said to be the snake in the Garden of Eden.
Lilith is the polar opposite of Eve meaning she is the polar opposite of Ninhursag, Lilith is the dark/satanic mother goddess(polar opposite of the mother goddess Virgo/Ninhursag) and is the queen of demons.
Samael/Satan
Samael
Samael is an archangel in Talmudic lore. He has been known as the seducer, destroyer, accuser and has been regarded as both good and evil in various texts. In rabbinic lore he was revealed as the chief of Satan's armies and as the Angel of Death.
His name means "Venom of God", suggesting he is either the vengeful hand of God or the enemy of God, and it has even been suggested that Samael is the angelic name of Satan himself. Lilith was created by Enlil(Satan) Who was the God of wind, Lucifer and Satan were two compleatly different beings because Lucifer was the xen energy form of Enlil and Satan is the nubilus energy form of Enlil. Samael(Samana is the Anunnaki name for Lucifer/Satan/Enlil) was a manifestation of apart of Satan's(Enlil's) consciousness.
Depending on tradition, Samael can be a fallen angel or he can be seen as an angel who is still loyal to divine law but enforces the darker side of faith (in either form he can be considered an alter-ego of Satan or a unique entity in his own right). He could be the embodiment of corruption and amorality.
Samael is Satan.
Satan
Satan is one of the Seven Princes of Hell. Before his fall, Satan was a Seraphim and a prince of the choir, showing his status as the supreme Seraph as Lucifer is over the Archangels. However, it is believed that Satan was something else before he was appointed as a Seraphim. He himself states that he is a bit of an enigma. Scholars state that Satan was an ancient spirit or force that existed when the first spark of creation was lit, possibly around or before the Earth was created. He is believed to have once been a wandering spirit with no purpose, confused of his surroundings and existence until God appointed him with being a judge. It was until then that he soon became a prince of the Seraphim.
When God commanded the angels to bow to the first human Adam, Satan (then an angel called Lucifer or Helel) rallied other angels against this command with the belief that angels are above all other creations. He and other "fallen angels" fought against the forces of God and were utterly defeated; as a result, Satan was cast down into Hell. After his fall, Satan became the King of the Inferno and the lord of all demonkind, surpassing even the nigh-omnipotent Lucifer. Despite having rulership over Hell, he remains imprisoned in the depths of the Abyss.
Contrary to popular belief, after the fall it is believed that Lucifer became a demon when his heart was filled to the brim with corruption and darkness. However, regardless of his appearance, Lucifer remains to be a fallen angel rather than a true demon. He is simply regarded as a demon due to his character and appearance. Satan, however, completely discarded his angelic origins and fully embraced his current status as a demon. So in theory they could be different, but really they are the same two different sides of the same coin.