There's two main differences between the two.
Disc Drive
The S doesn't have a disc drive, so you have to buy the games online and download them. There is a monthly subscription called xbox game pass, which will let you play lots of different games while subscribed, or you can you can buy each game individually, which you then own.
The X has a disc drive, so you can buy a game from a shop, take it home and put the disc in and play. (In theory, a lot of games you buy from a shop now don't even have a disc, its just a box with a bit of paper with a download code in.
Prettyness
The X is more powerful than the S. Both will play exactly the same games, (and I believe that Xbox have committed to that for the lifetime of the console), and the gameplay will be exactly the same on both. However the graphics on the X will look slightly better, whether that is because they're Ultra HD rather than HD, or have a higher frames per second (basically makes gameplay seem smoother)
Personally, I'd go for the S. As long as your internet connection isn't dreadful, then downloading games won't be a problem and I can see disc based games disappearing in the next 2 years anyway. The difference in graphics won't even be noticable to most people, especially if you haven't got the latest all singing all dancing massive TV.
This article is a good one for explaining the differences without getting too techy, feel free to @ me if you need any help