The demon Taraka had a boon that only a son of Shiva could kill him, and Shiva, after Sati's death, had gone back into meditation and wanted nothing to do with sons. The gods needed the god of desire. Kama went up to the mountain with the spring behind him, waited until Parvati came to lay flowers before the meditating god, and let fly his arrow. Shiva's eyes opened, and then the third one, and the fire from it left nothing of Kama but ash. His wife Rati wept over the ashes and rubbed them on her own body. Moved by her, Shiva gave what he could: Kama would go on living without a body, as Ananga, felt everywhere and seen nowhere, and in time he would take flesh again. He did, as Pradyumna, born to Krishna and Rukmini. The Matsya Purana carries the fullest and earliest telling.
The Shiva Purana gives Kama more swagger: he boasts of his power before he climbs the mountain, and the burning reads as pride corrected. At the end, rather than merely reprieved, he is absorbed into Shiva's own company.
What is different here:
Kama more arrogant; his fate is absorption into Shiva's retinue.
The Vamana Purana's Shiva is not a stone. Struck by the arrow he feels the loss of Sati anew and is shaken before the anger comes; the burning is the act of a god who has been hurt.
What is different here:
A more vulnerable Shiva; the burning follows grief, not only anger.
In parts of the south Holi is kept as the day of Kama's burning and is called Kama Dahanam or the festival of Madana; an effigy of the love-god goes into the fire and the songs are Rati's laments.
What is different here:
A festival re-enactment rather than a text; the burning becomes the spring bonfire.