Grenades are things you throw. With your hands. They have a pin you pull, with your fingers, and a lever/spoon that releases when you throw it, with your hands.
I will say that when you say "Mortars", it can be confusing because you can use the same word to refer to the gun and the munition.
The munitions are named Mortar Rounds. The tubes are just Mortars. So it can get confusing.
This is why we typically refer to the rounds by their sizes, even artillery rounds, to avoid that.
Ah, and to add-- while Mortars and Howitzers are both classified as "Artillery" and/or "Indirect Fire Munitions", we refer to Howitzers as Artillery and Mortars as Mortars, not artillery. Only because Mortars are typically a company level munition an--
You correctly referred to mortars rounds. Not mortars. Mortars are clearly the guns, not the ammunition.
Grenades. The addendum hand is often used. As grenades are not necessarily hand held. Hand grenades are. Others are not. They just denote shells filled with explosives.
Excluding mortars from the artillery department seems a priori counterintuitive, considering the historical use of super heavy mortars. But admittedly, the classical siege mortars have disappeared.
Or, you know, you can show your source that is apparently better than actual hands-on training, briefings, and the military shoving it down my throat for several years. I do enjoy civilians trying to tell me what my job is better than me and the SMEs with actual experience.