`find` supports an “or” disjunction, `-o`:
find . -type f \( -iname \*.tif -o -iname \*.tiff \)
This will list all files whose name matches `*.tif` or `*.tiff`, ignoring case.
`-print` is the default action so it doesn’t need to be specified here. `*`, `(`, and `)` are escaped so that they lose their significance for the shell.