The backing paper or sealing band will tell you what format it is. They made the difference very obvious so photographers and lab technicians could tell them apart at a glance. If it’s Ilford paper, there will be a black/white diagonal stripe pattern on the top and bottom edge, and the film name will have “220” beneath it. If it’s Kodak, there will either be “220” in big letters with horizontal lines between each repetition, or green cross-hatching along the entire width of the film with the film name being accompanied by “220”. I have yet to get my hands on any Fuji 220 paper but I suspect that it will also be marked distinctly.
However, with all that being said, you probably just have a roll of blank paper. 220 is usually fatter than 120, if only slightly. Not narrower. See attached picture for a comparison between 120 and 220 roll “fatness”.