NJ taxes wages differently than federal or NYS. Federal and NYS are identical(assuming 100% taxable in NYS).

NJ doesn't deduct pre-tax medical expenses, so NJ wages are higher then federal by that amount. Additionally, you can then ADD the pre-tax medical to the rest of your medical expenses for NJ only.

NJ also follows federal law for 401k deferred compensation, but NOT for 403b or 457 deferrals. This means that since NJ has already taxed the employee's contributions to those deferrals, there is cost basis to be allocated to the distributions when they retire.

Meaning, regular 401k distributions are 100% taxable to both federal and NJ, but 403b and 457 distributions are 100% taxable to federal but NOT to NJ. NJ has a 3 year recapture of retirement basis or an annual allocation of basis.

I almost forgot this part: However, the employer generated a separate W-2 for the state of New Jersey, and in Box 16 (State wages, tips, etc.), it shows a dollar amount approx half of what shows in Box 1. If they lived in NJ the entire year(or the entire employment during the year for that employer) then 100% of the wages should be in Box 16, subject to the adjustments above.

IN ADDITION, did she work at home in NJ during the year, and NOT in NYS? (Assuming it was for the convenience of the employer and not the convenience of the employee. Or some such nonsense.) That would allow some of the NYS wages to be prorated out of NYS. NJ should still be 100%.