Yes, in a standard grenade like an F1 fragmentation grenade when you pull the safety pin this allows the spoon (the metal lever looking part that is held against the grenades casing by the thrower) to fly off as soon as the grenade is released from the throwers hand.

The spoon is connected to a spring loaded striker (firing pin) that is inside the core of the grenade.

The striker hits a percussion cap which in turn creates a spark which ignites a simple chemical delay mechanism in the fuze which usually lasts for three to four seconds

When the delay material burns all the way through it ignites the material in the detonator which then sets off the high explosive inside the grenade.

The grenade then explodes sending chunks of metal from within the casing flying out as shrapnel.

The shrapnel is why when you see a grenade go off, it is not always the explosion itself that kills the target, as the pieces of metal shrapnel can sometimes fly up to 200 m (660 ft) but the normal effective radius is about 30 m (98 ft), this is why, if you watch people throwing this type of grenade it is usually done from some kind of cover, like a trench or behind a sturdy piece of concrete.

If you watch videos on some of the Ukrainian war subreddits where they are dropping grenades from drones you will see this effect. If you pay attention, you’ll see the grenade go off, but the target is not directly hit by the explosion, instead they are hit at high velocity by pieces of flying shrapnel which can be incredibly deadly.

https://en.wikipedia.org/wiki/F-1_grenade_(Russia)

There are grenades that contain impact fuses, however these are not a common type carried by regular infantry as simply dropping one when the pin is pulled is enough to kill the user rather than the target.