To further educate, be careful in trying to determine exactly what the other laser rods are. There are many types of glass materials used with Neodymium, or ND.
If one laser rod specifies ND:YAG, then yes, that rod is an Ytrium-aluminum-garnet glass rod, doped with the rare earth ion Neodymium.
As far as the other two lasers, they are laser rods doped with Neodymium, but take note that there are many glass types that Neodymium is added to. Example:
(phosphate glass):
potasium-barium-aluminum phosphate
aluminum phosphate
sodium-aluminum phosphate
(silicate glass)
lithium-aluminum silicate
alkali-zinc silicate
etc.
So, you can clearly see that there are many glass rod types, or crystals that use the rare earth ion Neodymium. The first indicator, is this ND:
This states that the crystal rod is doped with Neodymium.
The second note is :YAG
This states that the rods crystal makeup is Yttrium-aluminum-garnet
If the two other laser rods are not specified past ND:, then you need to check with the manufacturer as to what the crystal or glass is if you wish to truly know what the laser rod material is. Different laser rods are used in different applications. Note that each laser rod or crystal type, is not sufficient for every task, even though many may be doped with Neodymium.
So, in direct answer to your question, "ND glass laser, can this be correct"? YES, this is correct. It is simply stating that the laser rod or glass is doped with Neodymium. But, they are not indicating what type of glass is used to make the rod. This greatly limits your knowledge of what the rod is specificaly good for.
Some lasers are visible light, some are invisible, such as near infrared and infrared. Some laser assemblies, will incorporate the use of both visible and invisible laser light. The visible is used to target an object, where the invisible is the one that actually does the cutting. In the case of invisible laser light, a user must be especially careful, as you may not be aware of exactly where the light is. It will burn you quite badly before you even know it is there.
So, if you are to be the Laser Safety Officer, it is best to educate yourself as intimately as possible, regarding general laser theory, and most importantly, exactly what type of lasers you are dealing with.