@kittell17
Save just overwrites your current save. So does Save and Exit the game, Save and Exit to Manage Worlds and Save and Exit to the Main Menu. It does not accrue and it does not create separate new saves.
Save As lets you create a new save with a different name and it will accrue if you use it often. I use it to create a backup every time I play and delete the earlier backups. So I always have 2 current save files for just in case something goes wrong so I don't lose all my progress. I also play a big game with over a 100 households and most of my lots are now custom which I either created or downloaded from the Gallery. All of that is in a single save. I don't want to lose thousands of hours of play so I make sure I have backups of everything.
Keep in mind that the last file you saved, regardless of title, is the one that gets loaded the next time you start the game with the big arrow on the Main Menu. To load any other save, you need to use Load Game which lets you pick which save gets loaded.
As I said earlier, the Tray folder contains the items in your Library. Deleting them will usually not mess up your active game. It will just remove things from your Library. The dates associated with the files there are simply the date and time you saved a lot or household to your Library. Deleting anything there will delete them from your library. Each item in your library has multiple files.
I do not recommend that you delete files directly in either the Saves or Tray folders. You really do run the risk of ruining your current save or the items in your library if you do. It is much, much safer to use the in game methods to manage both your saves and your library. Everything you save in either folder creates multiple files for each save or library item. Deleting even one of those files associated to a save or library item will mess up whatever the thing was you saved.
If you still want to test the effects of deleting files directly though, I recommend that you make a copy of your entire Sims 4 folder and put it somewhere safe like on your desktop so you don't mess up your game if things go wrong. Then have at it to see first hand what happens.
Tbh, deleting files from either folder is not going to save you any appreciable drive space. What really takes up storage is cc. If you download a lot of cc and add it to your game, it can add up quickly. It also can have a detrimental effect on your game in a lot of ways. I do use cc and mods but I manage what I have and try to keep the amount down and only keep things I use regularly.
Another thing that can add up quickly is screenshots and using the in game photograpy. All those files are stored in the Screenshots folder. To max the photography skill, it takes between 90 and 150 photos per sim. You can delete those without a negative effect on the game except that any portraits you take will go black if the file it uses is deleted so you need to pay attention to what you are deleting.
Hope this helps you.
