PNG, like TIFF, is totally lossless. It's like a zip'd copy of the original image file.

JPG, is lossy compression. It deletes information from the original image, and compresses the result, giving a much, much smaller file. But it can never recreate all of the original image data.

[EDIT:]When creating a JPG file, one can specify the degree of data loss, aka "quality". Using 100% means no loss, but that's pretty rare. To get small files, one generally specifies 75-80% quality.

Cheers