Baladi, of my country. Comes from the country people who came to the cities and brought their dance with them. Low earthy movements, simpler and less staged than oriental.
YouTube - Yasmina of Cairo
Shaabi, of my people. Like pop, much more upbeat, cheeky lyrics, gritty and a bit 'street'. Hakim and Saad are shaabi.
YouTube - Saad el Soghair - hatgawez
At the extremes, the difference is easy to spot. In between, a huge grey area. Some will say things are one, some say they are the other.
The links are in relation to the music rather than the dance.
And there's so much more that could be said, but that's just a quick answer.