How do I explain to you that I am the source. I am the reference. I am the one who tells you what is right and what is wrong because I am the SME. You're just a civilian who reads the books we write.
Do you want to put on the clown paint now, or later?
Unless you're an individual with actual military experience who has worked directly with both mortar systems and howitzer systems, picked up and placed a mortar into a tube to fire it, and called in a fire mission utilizing both systems, then you are likely not experienced enough in this topic aside from what books will tell you.
I'm not arguing with a civilian over military terminology. That's a waste of time. Let me know when you sign up and then I'll actually take you seriously.
Don't you have manuals or of anything of that sort? There must be something written. Or are you telling me this is something only used in spoken language? If this use is so established, it should be easy to find.
Mortar: a workable paste to bind bricks, stones and cement by filling in and sealing gaps in between the building blocks; modern mortar is usually a mixture of sand, cement, and water