I hear instructors using awase tsuki or morote chudan in reference to a simultaneous strike to the stomach and face. I want to know if both phrases refer to the same strike pattern and if not which phrase is the correct one to use.
I would advise you to search the web for a glossary for your art - whichever it is. I've found a number of aikido glossaries, and I refer to them frequently.
My Japanese is rudimentary at best; others with better skill will correct me.
I've never heard of Chunad or Awazi, so I've supplied the closest sounding term from my experience.
Awase is a subtle word; I'm working on my awase in the koryu dai san tachidori, but I'm also working on the jo awase exercises. Sometimes I think I won't fully understand the word until I'm more advanced in the exercises.
Tsuki is thrust, and we use it when we strike with sword or jo. I believe I've occasionally heard it used to refer to a strike, but we more often use the word "atemi", (or "Uchi").
Japanese is like most languages - there are multiple ways to convey any concept, and more than one of them can be correct. Sometimes it depends on the specific nuance the teacher is trying to convey, sometimes it depends on where they originally learned the technique. Sometimes it depends on the kata in which the technique takes place. Sometimes it is simply where the teacher's mind is at that moment. There is no formal grammar of movement.
Personally, I'd assume that whoever is teaching me is using the term correctly.
In Seido Karate these are two different techniques.
Morote Zuki is a double punch to the same level (Jodan/Chudan/Gedan). see image here
Awase Zuki is a combined middle + face punch see image here