@lizzie_7654You have folder The Sims4 in Documents. In this folder you have many subfolders.
Your saved games are in the Saves folder.
Tray folder - it is your library. When you are saving something to library you see only the image of it in Gallery but saved files are going to the Tray folder.
In fact, all of this you see are only displayed images of the files you have in the Tray folder.
The same is with files of your saves folder. When you press the Load Game button you see only images of files that you have in your saves folder.
But selected files in this folder cannot be deleted - just like that - so they still need to be in the saves folder. Only these files are not displayed when you press the "Load Game" button.
As if the game did not see these files - in other words, the game does not see your saves.
When the game folder is moved the game creates a new empty in its place so there would be no option to see these old saves. So it must still be in your game folder and I'm trying to find out the reason why the game - or computer - can't see these files.
I see you are feeling not comfortable with idea moving folders to the desktop. (Folders are these yellow books, files are inside it and look like pages.) So forget about it.
Go to the Origin, select My game library and right-click on the cover of TS4. Select the option "repair game" and press it. You have to wait until Origin will fix all packs, not only the base game.
But there is a weird option also that the computer is seeing only the old folder but you are playing in the second one that is in another place where the computer can't see it.
Go also to the game and take some screenshots when playing. These screenshots will go to the same place where saves are. Then try to find your second game folder (if it is existing but you are not able to see it). Instructions are here
https://sims4.crinrict.com/eng/2018/07/how-to-find-your-user-folder/ 
