From Destinypedia, the Destiny wiki
Grenades are one of the three core aspects of a Guardian's Class and Subclass, alongside Super and Melee abilities. Grenades are normally thrown a certain distance, and detonate upon hitting the ground or a foe, usually inflicting Elemental damage in an explosion, and often applying other effects, depending on the Subclass. In Destiny, Grenades were restricted per Class, with one shared, but in current Destiny 2, all Grenades are shared across Classes.
Grenade cooldowns are modified by Discipline. The effects of Grenades can be further modified by passive abilities, Aspects and Fragments. Several Mods and Exotics also alter or benefit from Grenades.
Most enemy races have access to Grenades, usually wielded by low ranking members of the faction. Fallen Dregs use Shock Grenades and Vex Hobgoblins use Slap Grenades in Destiny, while in Destiny 2, in addition to the above, Cabal Legionaries have their Cabal Frag Detonators, Hive Acolytes have Acolyte Grenades and the new Scorn Stalkers use Scorn Grenades. In addition to this, Ultra enemies may have the ability to use their brethren's Grenades even if not of the same class, like Phry'zhia, the Insatiable in the Grasp of Avarice Dungeon.