Find files whose basenames are the same, but their ext names are not

If you have GNU uniq, you can sort case insensitively (-i), and use -d to print only duplicate lines:

find . | sort -f | uniq -di

As @StephaneChazelas mentioned in his answer, this might not do what you expect if you can have duplicate paths that only differ in case (like a/b/foo and A/b/foo).

I'd suggest a different approach, avoiding the possible word-splitting issues of ls

#!/bin/bash

shopt -s nullglob

for ext in jpg png gif; do 
  files=( *."$ext" )
  printf 'number of %s files: %d\n' "$ext" "${#files[@]}"

  # now we can loop over all the files having the current extension
  for f in "${files[@]}"; do
    # anything else you like with these files
    :
  done 

done

You can loop over the files array with any other commands you want to perform on the files of each particular extension.

More portably - or for shells that don't provide arrays explicitly - you could re-use the shell's positional parameter array i.e.

set -- *."$ext"

and then replace ${#files[@]} and ${files[@]} with $# and "$@"