Free spell

Free spell is Magic jargon for a spell which can be cast without paying mana for it. Free spells usually have an alternative casting cost.

Examples

Pitch spells
The seven one-mana spells and two X-spells which have phyrexian mana costs.
Spells from the Masques block which may be cast for free if the controller and an opponent control lands of a certain type.
Time Spiral Pact cycle cards, which have a mana cost of , but require the caster to pay mana at the beginning of their next upkeep or lose the game.
Commander 2020 commander discount cycle spells, which can be cast without paying their mana cost if the caster controls a commander.
Modern Horizons 3 cycle with alternate cost of sacrificing a nontoken creature that shares a color with the spell.

Many cards allow another spell to be cast "without paying its mana cost", but these enablers usually have a significant mana investment of their own.
Although spells with the free mechanic from the Urza block are commonly known as "free spells", since the net effect is having the same number of lands untapped, they are not free, since they cost mana to cast, and the land untapping effect only happens if they resolve.