Image file format questions

Here are 2 questions for you guys:

1) Today in my Imaging class, we were taught that 'file size' and 'size on disk' were different because 'file size' is the raw data of the file, and 'size on disk' is the whole size including file header/tags. I always thought it had something to do with clusters, but my teacher was having none of it... which is it?

2) We were also made to do an exercise using the TIFF format for saving indexed colour in decreasing amounts. The decrease in filesize from 256 to 128 colours was rather large as expected, then upon saving in 64, 32, and 16 colours, the file size was pretty much the same as 128. Why is this? Again, the teacher said this is due to lots of tags in the file header. He didn't elaborate, leading me to think he could be wrong.

Thanks in advance, and excuse my ignorance.

So, Photoshop is using 7-bits for <128-color indexing... and nothing at all to do with "lots of tags in the header bumping up the filesize".

This probably isn't true. What is true is that you shouldn't try guessing what's going on in there, since image compression depends on a number of variables (as well as the algorithm). Unless you know how TIFF works, you're better off not assuming anything. Your professor is probably wrong regarding headers though.

PS. Photoshop really is shitty when it comes to image compression. You'd expect the premiere raster editing program to do this well, but nooooooo...