# sort the first file by the second column (zero-indexed)
sort -n -t , +1 f1 >s1

# sort the second file by the second column (zero-indexed)
sort -n -t , +1 f2 >s2

# print lines whose second column (one-indexed)
# are common to both files
join -t , -1 2 -2 2 s1 s2

# print lines in file 1 that are NOT in file 2
join -t , -1 2 -2 2 -v 1 s1 s2