There will be four speeds of movement in the initial release including sprint, run, walk and crawl. Sprinting for a long distance will eventually force you to run. Running will be slightly slower than sprinting. Both sprinting and running will be significantly faster than walking. Crawling will primarily be reserved for moving under objects or if your player has been crippled.
Your player's movement speed will not impact your hunger directly, but it will further decrease your thirst.