They were equivalent to the western allies' armoured infantry or the Soviet's mechanized infantry divisions, but due to the Germans lack of armoured transports and motorized vehicles, they were not much better equiped than regular British or American infantry divisions which were fully motorized.
One must not forget that the bulk of the German army were foot soldiers supplied by horse drawn wagons during WWII!
Panzer is German for amour. The grenadiers were originally infantrymen that carried and threw explosive bombs ignited by a fuse. The term grenade had its origin from the pomegranate fruit because of its resemblance to it. Later on the term were used for elite or guards units. Thus it would be more accurate to say that Panzer Grenadiers were guards infantry units transported by armoured vehicles instead of grenade throwers.
On paper they were supposed to be transported by armoued halftracks, but only one batallion were supplied and the rest were motorized infantry.
By the way, t3488g, where is that halftrack parked? The color of the halftrack looks like Testors MM Sand Grey instead of Testors MM Dark Yellow. I have seen information that claims that the Sand Grey is the correct color for Dunkelgelb, and that MM Dark Yellow is wrong.