I think it's important to note that many of these overlap with each other as they are socially defined, as opposed to defined by action. Even among the action defined ones like emotional and sexual, what falls into what people consider "sex" or what feelings are on or off the table because of existing relationships and desires, are all malleable to an extent.

Romantic is the most socially defined among this list, and broadly overlaps with all of these categories. It's also the category among these I struggle the most with, as I don't do well with broadly/loosely defined social concepts, especially those that often come from the experience of a feeling (gender is another example of these). It's less likely that one person's definition of an intellectual connection/attraction would differ significantly from another human, but much more likely that romantic would.

At the end of the day, language isn't perfect. It's a way for us to communicate abstract ideas with some kind of structure. Ultimately you need to ask someone what romance is to them, to understand whether that's something you're interested in, and then have a conversation with the person about what kind of romantic connection they are on board for.