This reminds me of the discussion Shabook and I had about Helicopters and Choppers. To me, the difference between A-Bombs and Nukes were the usage of Hydrogen vs. Uranium. However, Jarvis disarmed a uranium core, making it a nuke to me.
I agree with your change, if you make it and will write a expanded history, if the change is approved. (Don't forget to add the appropriate categories, if you do it.)
I was going to create an Article called "Weapons of Mass Destruction" to cover all the Nuclear, Biological, Chemical, and Tesseract-Powered weapons seen in the MCU. To answer your question, an A-bomb utilizes nuclear fission, typically with a Uranium or Plutonium atom. An H-bomb, thermonuclear bomb, etc., uses fusion, where hydrogen atoms fuse into helium. They're a lot more destructive.
And, on a related note, those "flying atomic bombs" AKA HYDRA Parasits, are not atomic bombs, nor are they nuclear in any sense. They appear to be antimatter-based, given the clues provided in-universe.