Mainly because the DVD-player works by buffering the video-imaging into a RAM, which then is read when playing the video.
A VHS-still works by halting the tape and continuously reading a requested frame (of maybe 1 ms), which is edged magnetically into the tape. In other words; the head reading the tape has to read that 1ms (it's certainly more than just 1 ms BTW.) over and over and over again until you unpause. Thus the head renders the data read from the tape as it reads just a slight portion continuously => creating a shaking effect = the same frame rendered over and over again.
A DVD-still on the other hand works completely different, as it works by buffering the video-imaging into a RAM, which then is read when playing video. This buffering of data is halted when you press "still", and the data portion rendered into the RAM is being displayed the same way a PC displays an image: simply not changing the pixels from their altered state.
That's the gist of it, at least