Fuse is means to attach something to something else and create something new out of it. Commingle means to mix a collection of separate objects together. Merge means to combine two things together similar to fuse, but I would probably use this word when describing a less “complete” combination.

They all pretty much mean to blend separate things together, but you would use them all in different situations. They are what we call Synonyms of each other. Synonyms are different words that mean the same thing or pretty close to the same thing.