I'm attending a conference this summer at the S&D. Does it matter which hotel I book my room in? I have no idea which hotel the meetings will be held in, and I've never stayed at or visited the S&D so I have no point of reference. Thanks!
It's certainly not a long walk between the two. Unless you're slowly strolling it's maybe 3 minutes from door to door.
Take a look at the satellite view to get a lay of the land:
https://www.google.com/maps/search/walt+disney+swan/@28.3663915,-81.5609674,1056m/data=!3m1!1e3
I've only stayed at the Swan, which is smaller (fewer rooms). The Swan is run by Westin I believe, and the Dolphin run by Sheraton. I'm sure someone will correct be if I flipped those.

The only difference I know of that would factor into which one I book is that the dolphin has double beds in the rooms with two beds, the swan has queen. That's why I book Swan for my family of four. In Sept, DW and I will hopefully get a trip to WDW by ourselves and I have the dolphin booked for that.