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.

OK, I had a go at reducing the colors in the same images he used, and I got similar results as >>13 ...which is fine, just means the instructor fucked up.

TIFF definately supports indexed colour, it just doesn't seem to reduce the filesize under 256 colours... which again, I can live with.

Now I'm back to the problem of file size vs size on disk. Can anyone explain these file sizes to me?

Colours -  Size   - Size on Disk
  256   - 278,036 - 278,528
  128   - 278,008 - 278,528
   64   - 278,036 - 278,528
   32   - 277,996 - 278,528
   16   - 278,088 - 278,528
    8   - 278,156 - 278,528

So... all the 'Size on Disk' sizes are the same, understandably, but why are the 'Size' ones different? I'm guessing this is why my instructor thought that 'Size' doesn't include file header tags, but 'Size on Disk' does.

Any ideas?