@JeremyDavies -- Thanks for the question! It's not a silly one, and we know we aren't going to get everyone to do it the "right" way in all situations, so we try not to make a big deal of it most of the time. 🙂
Our classic product is Esri Story Maps. The current generation product is ArcGIS StoryMaps. This is one reason why you might see it written differently. When you create a new item with ArcGIS StoryMaps, it's called a StoryMap (see screenshot, below).
If you're writing about the things you create with either of these products, we think it can be much simpler to just call them stories to avoid the whole issue. But if you prefer to use the full name, like in your example, I would suggest you use StoryMap.
Owen Evans
Lead Product Engineer | StoryMaps