How to detect files with the same name but different extensions?

I have a directory whose files have extension either .JPG or .NEF and I want to delete the files of the form X.NEF for which X.JPG does not exist in the directory. (X here can be any string.) I don't know how to do this other than by hand.

A more general situation is when you want to find all the files in a directory A which exist in directory B as well. (The first problem can be turned into the second one using mmv.)

You can use the shell's ${var%ext} parameter substitution features to remove the original extension on a per-file basis: to illustrate

touch file{1..6}.NEF file{1,2,4,6}.JPG

Then

for nef in *.NEF; do [[ -f "${nef%.NEF}.JPG" ]] || echo rm -- "$nef"; done

results in

rm -- file3.NEF
rm -- file5.NEF

Explanation:

The first command just creates 6 .NEF files numbered file1.NEF to file6.NEF and corresponding .JPG files for 3 of them i.e. just some empty files to test the second command on.