Molasses is basically what's extracted from raw sugar to make it white sugar. Brown sugar is sort of in between, they've taken some of the molasses out but not all, hence why it's brown and a bit moister than table sugar and has a bit more flavor to it (although I have heard that nowadays a lot of brown sugar is just white sugar with some syrup added back). Molasses is still sweet, but it has a distinct flavor as well and it's not technically sugar. More of a sugar by-product if you like.
Sometimes even though something is not sugar-free it can be useful, for adding a bit of flavor, a little sweetness without as much carbs as sugar, etc. This might be one of those cases. I mean if the total carb is still 2g per muffin, the fact that some of those 2g come from a sugar product wouldn't change much, would it? Technically Splenda has gram for gram as much carbs as sugar. It's just that it takes a lot fewer grams of Splenda to achieve the same sweetness as a lot more grams of sugar, so in the end you're reducing the carbs. It's not so much where the carbs come from, whether it's "a type of sugar" or not, as it is how many of those carbs you take in and what they do to you afterwards.