The Right stuff doesn’t take into account the struggle that is the lack of water on space and thus it was not made aware to us how the astronauts received water. This was rectified in the The Martian where a drop of sweat or urine was not wasted as it all went into the water reclaimer to produce the water they needed for survival
Although in both movies, the astronauts wore spacesuits, the spacesuits in The Right Stuff were costumes made by the costume department, those worn in The Martian were the space suits used by actual NASA astronauts. They allow for flexibility, comfort and reliability so as to easier navigate Mars and the long treks that would have to be made during the period of their space