Do horse grenadier and grenadier in Napoleonic age fire real grenade?

Question

If do, then explain the structure of the grenade they fire?
I see in some film, the horse grenadier seems to be file only solid bullet, and not grenade, then why they were called grenadier?
Is it true that all the horsemen is Napoleonic Age carried a gun and pistol, or just a sword and sabre?

Answer 1

The first grenades were small iron spheres filled with gunpowder fused with a length of slow-match, roughly the size of a cricket ball or a baseball. The grenadiers had to be tall and strong enough to hurl these heavy objects far enough so as not to harm themselves or their comrades, and disciplined enough to stand at the forefront of the fight, light the fuse, wait, and throw at the appropriate moment to minimize the opportunity for the enemy to throw the grenade back. Understandably, such requirements led to grenadiers being regarded as an elite.

Answer 2

remember when you played super mario 2 and you had to fight that rat with bombs? those bombs are roughly the same design as 18th century grenades.