I noticed that text surrounded by tildes in org-mode turns grey (as least in my colour theme, and I assume the colour changes in others as well). What is that about?
Tildes are used for marking something as code/monospace. See Emphasis and monospace in the Org manual.
Your whole buffer might be monospace in Emacs (depending on your settings) so the gray is a useful distinction. If you were to publish the file as HTML that text would be surrounded by