As you've already found out LR has no SAVE button. That's because every change you make to an image is stored in LR's database. If you want to push these changes out to the file (jpeg or DNG or XMP in the case of RAW) then you can choose save metatdata to file from the metadata menu or press Ctrl+S.
You can also turn on Automatically write changes into XMP on the Metadata tab of your catalog settings. This will write all changes out for you.
Now, until you export your image to jpeg or TIFF or PSD, etc, the changes aren't "baked in". The point of LR editing is to be non-destructive so the database remembers everything you did.