there's something funny going on all right
my full screen shots are about 3MB
They are same size whether 8 Bit or True Colour - actually I dont think that's funny - just that your "TIFF's" are so small ...
My ancient Photoshop 5.5 cant open the 8 Bit or the larger true colour TIFs which surprises me cause I usually work with TIF scans from various sources and have no problems

maybe I just need to reboot ..
Photofiltre has no problem with either
both programmes can save a much smaller TIFF version than S.C. (in Pshop if LZW compression is selected, in P'filtre via default save)
EDIT/btw:
the problem with opening the tiff seems to be with the system here somehow (now having problems with other tiffs with another programme)