Rocket artillery is unguided, meaning that once it leaves the rails it is not corrected in flight. You will occasionally see the term "Katyusha" used in news stories although the ordnance under discussion isn't the old Soviet Katyushas of WWII fame at all. Sort of a generic term these days and I wish they wouldn't use it.
Basically the term "rocket" refers to an unguided projectile and "missile" to a guided one but there are various forms of guidance, both internal and external, that act at different times. To confuse the terminology further "ballistic missiles" are so called because although they are initially guided part of the flight path (usually the extra-atmospheric part) is "ballistic", meaning unpowered and uncorrected, although the payloads of such weapons can be corrected in their terminal phase.
The weapons we're talking about here have neither internal nor external guidance systems - they're fire in a direction and forget. Crude weapons, employed in regular warfare only in multi-missile barrages to saturate the target area (hence "artillery"). In individual firings they are useful only as terror weapons, part of the terror resulting from the fact that they can hit pretty much anywhere downrange. If the trajectory is high enough they'll fly until they run out of fuel and coast to the ground. If not they'll still be under propulsion at impact.
If it doesn't make sense...well, that's the military... ;-)
OK, from what you say, I can see that military usage is quite different from not only the dictionary, but also from the usage of Physics, the basic science involved. SNAFU, I guess.