If you worked in NY full-time, then all the income for NY in boxes 15-17 are correct. They should match the federal amount in Box 1.
NJ is weird. They tax contributions to cafeteria plans, HSAs, retirement accounts that are not 401(k)s that fed and NY do not. That means your taxable NJ income is often higher than NY or federal. The amount your employer is reporting as NJ income may be the additional wages that are not taxable federally or by New York.
If that is the case, then you would want to report the full amount reported as NY wages on your nonresident NY return. On your NJ return, your total wages are what was reported on NY plus the additional amount for NJ due to the items that are taxable in NJ but not elsewhere. Your NJ resident income from this job will be the amount reported to NY, which matches the federal, plus the amount reported as NJ to account for the state's different tax laws. You will get a credit for the taxes paid to NY on your NJ return.
