Does casting a spell for its madness cost count as casting it from your hand or from exile?

When you discard a card with madness, a two-step process occurs. First, instead of going to the graveyard, the card is exiled face-down (CR 702.36b). At that point, the card has left your hand entirely and now exists in the exile zone.

Second, you get a triggered ability that lets you cast that exiled card for its madness cost (CR 702.36b). If you choose to cast it, you are casting it from exile, not from your hand. The card never returns to your hand at any point during this process.

If you choose not to cast it for its madness cost, it simply moves from exile to your graveyard — again, never back to your hand (CR 702.36c).

This distinction matters for effects that care about spells cast from specific zones. For example, if you control Containment Priest (which exiles creatures that enter the battlefield without being cast from hand), a madness creature cast from exile would still be 'cast,' so Containment Priest would not trigger — but any ability that specifically requires a spell to be cast from your hand would not be satisfied by a madness cast.

Practically: effects like 'whenever you cast a spell from your hand' will not trigger when you cast a spell via its madness cost, because the casting happens from exile, not from hand.