That's probably because your DVD player is rendering them. When I watch a movie with subtitles in VLC I get really nice smooth Helvetica.
You are probably watching video files with subtitles as embedded (or separate) text files (srt etc). This allows the video player to render them with any font and higher resolution.
Not all DVDs have both, although a lot do. Some have just one or the other.
So closed captions have stuff like "door opens, a radio is playing an old tune in the background. Sheila: Hello" but with subtitles you'd just see "Hello" since if you can hear then you can infer everything else about the scene.
"Subtitles" on a DVD are basically a 4-colour (3 + transparent) bitmap which is overlaid on the video stream. But DVDs also support the closed-captioning that was originally used for TV broadcasts, which is text embedded in the video signal that's decoded and displayed by the television set itself.
Media playing software can extract subtitles from the latter system and display them in whatever font you like - but you can't do the same with the DVD-overlay subtitles, because they're just images.