What is JPG?
JPEG is where photographs live. Its compression is lossy - it throws away detail the eye is bad at noticing, and throws away a bit more every time you re-save - which buys huge size savings on photos and makes a mess of screenshots and text. There's no transparency in it at all.
What is TIFF?
The format print shops, scanners and archives run on. Lossless, capable of holding several images in one file, and old enough that everything in that world reads it. Files are large, which nobody in print has ever minded.