Work in NJ - live in NY.Get 2 w-2s from same employer. Box 1-13 is the same, 15-20 are diff. Box 14 says NY WAGES W-2 DATA is on Separate W-2. what category for box 14?

You do not need to enter that Box 14 information into your return.  Box 14 information is mostly informational.  There are a few categories of information placed in Box 14 by employers that does need to go to other places on your return.  In this case though the information is purely FYI.  Box 14 would label the information to match the categories you see in TurboTax if it were applicable. 

In case you weren't aware...When you have duplicate W2s with differing state information you only need to enter one W2 in TurboTax.  You will have two lines of state information in TurboTax W2 entry page.  Enter your NJ state information then "Add a line" and enter your NY information from the applicable paper W2s you have.

NJ will tax your income earned in NJ as a non-resident and NY will tax the same income as a resident.  On your NY return you will need to go through the "Credit for taxes paid to another state" topic to get credit on your NY return for taxes paid to NJ on the same income.