There are plenty of people who only really played singleplayer, but those people are not likely to be active online in forums about the game, so, definitely the multiplayer. The competitive scene, LAN parties, and also the custom games (Use Map Settings) scene was huge. There was a time I invited a friend over to play StarCraft multiplayer he assumed I meant to play custom games, not regular 1v1s. Kind of like how in Warcraft 3's time, more people were playing DOTA (back when that was only a thing inside of Warcraft 3) than were playing the actual multiplayer, though not as extreme.

Also a lot of people say "Brood War" to mean "SC & SCBW," especially because now people will assume "SC" refers to SC2. Back in the day sometimes people would say "vanilla" to mean SC1 without Brood War.

I agree that the SC1 campaign story is better than BW. But also if you see praise for BW, you can remember that a lot of people played the games when we were kids and weren't really able to judge high quality writing. So like if I say the story in BW was better than the story in SC2, you can take it with a grain of salt because the first one I took in completely uncritically as a kid, and the 2nd one I didn't.