With GNU grep:
grep -wo '[Oo]range' filename | wc -l
Here the -w makes it only match whole words; the -o makes it split each occurrence of a match on the same line into its own line and suppresses other output, and the expression will match "Orange" or "orange".
This is then passed to wc which counts the words. Since each is on its own line you could use wc -l or wc -w and the results will be the same.
