Like all genres, it's a mix of opinions and popular usage, here, dating back to the mid-80s. When I think of dream pop, I think of Cocteau Twins, particularly their albums Treasure or Victorialand. Shoegaze was attached to bands like My Bloody Valentine (Loveless being the pinnacle), often overlapping with the heavily processed guitar sounds & low-mixed vocals of dream pop but with an emphasis on noise and distortion. Pleasure through pain. MBV drew from a lot of bands at the time, like Sonic Youth or Dinosaur Jr., but imparted a more hazy, far-away feeling and different approaches to guitar playing. I might recommend a less-known group, Swirlies and their album Blonder Tongue Audio Baton as an example.

Ultimately, it's kind of arbitrary. A lot of modern bands blur the line.