What each method throws away
Lossy compression analyzes an image and removes information it expects you will not notice, usually fine texture and subtle color shifts. The result is dramatically smaller than the original, and the removed data cannot be recovered. Saving the file again repeats the process and removes a little more.
Lossless compression finds patterns and stores them more efficiently without discarding anything. Opening the file rebuilds the exact original data, so a lossless image can be edited and re-saved indefinitely with no drift. The price is that photographs stay much larger than a lossy file of the same picture.
Where you see each one
JPEG is lossy from start to finish, and the quality slider decides how much gets dropped. PNG is lossless, which is why screenshots and logos stay perfect but photographs balloon in size. WebP offers both modes in one format, so you can choose per image.
The difference is easy to spot once you know where to look. Lossy compression shows up as blocks, ringing around edges, and smeared texture when quality drops far enough. Lossless files show none of that, but they fill storage and slow uploads faster.
Which one to choose
Default to lossy for photographs and anything that only has to be looked at. The quality loss is usually invisible at sensible settings, and the file travels much better over email and messaging apps. Use lossless when the image will be edited repeatedly, contains text or sharp lines, or must stay exact.
When a file must fit a size limit, lower the quality before you give up pixels. That keeps dimensions intact while pulling the file down, which is exactly what a compressor with a KB or MB target does. Keep an original copy whenever you expect to edit the photo again.