Some people consider Twin Flames to be a type of soulmate, because they are both soul connections and they both have quite a few similarities. However, in my experience (and from what I've read and other TFs I've talked to) meeting a soulmate is typically a pleasant experience. You find you just click with them and feel good around them.
With a Twin Flame, there is a magnetic attraction, but one that typically doesn't make any real sense. They aren't your type, even if you don't really have a type. You can't quite figure out why you are so drawn to them and the feelings are both overwhelming and confusing. Being with them in person may feel nurturing and joyful, but the relationship itself is typically a lot more fraught - in part because it makes no sense for you to want each other, the circumstances are all against it, you are vastly different in many, many ways, and yet - you still feel that magnetic pull. This is because the TF relationship is like a Yin/Yang symbol. You seem like opposites, with just a drop of the other inside of you, but you fit together to make a larger and more cohesive whole. A soulmate is someone who is cut from the same energetic cloth, so the relationship makes more sense and doesn't feel so chaotic.
Hope that helps and thanks for reading.