TIFF files

When would someone opt to send a client a TIFF file? And when sending a flyer that will mostly be used for web, should it be sent via PDF or JPG?

You do not normally send a client a TIFF unless they specifically ask for one. A TIFF is a high quality, print quality raster based format, ideal for saving photos that are then going into layouts in indd or ai, and then the final product will be exported as a PDF. T
Flyer for web would normally be sent as a jpg for best optimization, but you have a range of quality in jpg options so be sure to choose one that is the best combination of quality and low file size, based on your needs.