Did some brief (and nerdy) research on Grenadiers. 
A Grenadier was a special role from the 1600's.
They were trained in the use of grenades, assaults and sieges.
The word grenade is of Spanish origin; 'granado' which is a pomegranate, the size of the early grenades.
These guys had to carry big bags of cast iron grenades, which were lit using a tool that contained burning rope to light the fuse.
They had to be physically strong to throw the grenades far enough, and assault, so only big, strong guys were employed in the role.
They were considered heavy, elite troops, and to show this and make them more imposing during assaults, they had very tall hats, and some were encouraged to grow huge moustaches.
Grenadiers started attaching slings to their muskets so they could quickly shoulder it to throw grenades (the origin of rifle slings?).
They were sometimes armed with swords and sometimes axes to help hack down defences.
For a time the British army had grenadier cavalry (not long...maybe the horses were skittish near exploding grenades?).
Grenadiers were eventually organised into their own dedicated companies, battalions and even regiments.
From what I can tell, in WW2 German infantry units were originally called 'Schützen'.
Schütze means 'one who shoots', and was used for ordinary rifleman.
Then in 1942, Germany's motorised infantry were renamed Panzer Grenadiers, and their infantry were renamed Grenadiers.
The reason appears to be purely propaganda and bravado, because historically Grenadiers were the big, tough specialist troops.
No real change to equipment, training or organisation - just the name.
I wonder if the Soviet and UK 'Guards' divisions were named arbitrarily for the same reasons. Maybe some.
Would units that were named 'Grenadier Guards' be doubly effective?

As a side note, Fusiliers were troops that were given advanced weaponry (such as 'fusils' a new type of flintlock musket in the 17th century).
One of the roles they performed was guarding and escorting field artillery guns - because they were less likely than matchlock muskets to accidentally ignite open barrels of gunpowder!
A Grenadier was a special role from the 1600's.
They were trained in the use of grenades, assaults and sieges.
The word grenade is of Spanish origin; 'granado' which is a pomegranate, the size of the early grenades.
These guys had to carry big bags of cast iron grenades, which were lit using a tool that contained burning rope to light the fuse.
They had to be physically strong to throw the grenades far enough, and assault, so only big, strong guys were employed in the role.
They were considered heavy, elite troops, and to show this and make them more imposing during assaults, they had very tall hats, and some were encouraged to grow huge moustaches.
Grenadiers started attaching slings to their muskets so they could quickly shoulder it to throw grenades (the origin of rifle slings?).
They were sometimes armed with swords and sometimes axes to help hack down defences.
For a time the British army had grenadier cavalry (not long...maybe the horses were skittish near exploding grenades?).
Grenadiers were eventually organised into their own dedicated companies, battalions and even regiments.
From what I can tell, in WW2 German infantry units were originally called 'Schützen'.
Schütze means 'one who shoots', and was used for ordinary rifleman.
Then in 1942, Germany's motorised infantry were renamed Panzer Grenadiers, and their infantry were renamed Grenadiers.
The reason appears to be purely propaganda and bravado, because historically Grenadiers were the big, tough specialist troops.
No real change to equipment, training or organisation - just the name.
I wonder if the Soviet and UK 'Guards' divisions were named arbitrarily for the same reasons. Maybe some.
Would units that were named 'Grenadier Guards' be doubly effective?

As a side note, Fusiliers were troops that were given advanced weaponry (such as 'fusils' a new type of flintlock musket in the 17th century).
One of the roles they performed was guarding and escorting field artillery guns - because they were less likely than matchlock muskets to accidentally ignite open barrels of gunpowder!