Program which compares two files and print the same line

If duplicated lines in a file are allowed, you need a counter. Give this a try:

awk 'NR==FNR{a[$0]++;next}a[$0]-->0' f1 f2

Let's have a test with your data:

kent$  head f*
==> f1 <==
DGD1 SOL3605
DGD2 SOL1176
DGD2 SOL1598
DGD2 SOL63

==> f2 <==
DGD1 SOL3605
DGD1 SOL3605
DGD2 SOL1176
DGD2 SOL1945
DGD2 SOL63

kent$  awk 'NR==FNR{a[$0]++;next}a[$0]-->0' f1 f2
DGD1 SOL3605
DGD2 SOL1176
DGD2 SOL63

Based on one possible interpretation of your question:

$ sort -u file2 | awk 'NR==FNR{a[$0];next} $0 in a' file1 -
DGD1 SOL3605
DGD2 SOL1176
DGD2 SOL63

or awk only:

$ awk 'NR==FNR{a[$0];next} $0 in a{print; delete a[$0]}' file1 file2
DGD1 SOL3605
DGD2 SOL1176
DGD2 SOL63

Could you please try following. Written and tested with shown samples in GNU awk.

awk 'FNR==NR{arr[$0];next} ($0 in arr) && !arr2[$0]++' eq3_dgdg_1.ndx eq3_dgdg_2.ndx

Explanation: Adding detailed explanation for above.

awk '                             ##Starting awk program from here.
FNR==NR{                          ##Checking condition FNR==NR for first file processing.
  arr[$0]                         ##Creating arr with index of current line.
  next                            ##next will skip all further statements from here.
}
($0 in arr) && !arr2[$0]++        ##Checking if current line present in arr AND current line coming first time in arr2 then print it.
' eq3_dgdg_1.ndx eq3_dgdg_2.ndx   ##Mentioning Input_file name here.