Sanding solid stain off

You can likely answer your own question with a little experiment. Before committing the whole deck to large amounts of stain application try a small area on 1 or two boards where you've sanded on one side and the weathered grey is still on the other side. If you like the result you will know what to do. If you dislike the look or match then you can proceed to close up the stain can and go back to sanding and scrapping the rest of the deck surfaces. The place where you put the stain sample over the weathered grey can be sanded down to fresh wood right along with the rest of it.

You'll probably want to rent a proper floor sander. A small random-orbit will take ages and you'll probably burn through most of its useful life.

The sander should come with a variety of paper grits. As with any woodworking project, start with the heaviest and transition to the finest. The final should be somewhere in the 100-120 grit range.

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How far you need to go depends partly on the stain color--is it markedly different from the current color? Is it dark? Dark stain is more likely to compound if it's not completely removed. You'll see the old stain through the new as dark streaks or patches.

If you go the route of renting a sander, the work will be easy enough that you can get through the old stain without much effort, and you'll be confident of achieving a good result.