Reciprocal agreement between New Jersey and Pennsylvania.

NJ and PA have a reciprocity agreement which mean you pay taxes on your wages only in your state of domicile (home-state). since these wages are not taxed by the other state you get no tax credit in your-home state. 

income other than wages earned in the non-home state is taxed by both states but then you get a credit in your home-state. the credit can be less than the taxes you paid in your non-home state. you need to review the form on your home-state return to see how the tax is calculated 

The Reciprocal Personal Income Tax Agreement between Pennsylvania and New Jersey means compensation paid to New Jersey residents employed in Pennsylvania is not subject to Pennsylvania income tax. Therefore, you cannot claim a credit on Schedule NJ-COJ for taxes paid to Pennsylvania on those earnings. New Jersey residents can claim a credit for taxes paid to Pennsylvania on other types of income (for example, business income) that are taxable in both states by completing Schedule NJ-COJ.

The New Jersey/Pennsylvania Reciprocal Agreement does not apply to income or wage tax imposed and collected by the City of Philadelphia or any other municipality in Pennsylvania. That means a New Jersey resident who works in Philadelphia and pays city wage taxes can claim a credit for the taxes paid to Philadelphia.

The NJ credit is not a percentage of the tax paid to the other jurisdiction. It's the amount of NJ tax that you would have paid on the income if it had been NJ income instead of PA income. You can see the calculation of the credit on Schedule NJ-COJ in your New Jersey resident tax return.

The credit and the reciprocal agreement are two separate things. You use one or the other, not both. Which one applies to you depends on whether your PA income is from a job where you get a W-2, or from any other source. If you are a W-2 employee you should not have paid any Pennsylvania state income tax. Under the reciprocal agreement between NJ and PA you pay tax only to the state that you live in. If PA tax was withheld from your pay you have to file a Pennsylvania nonresident tax return to get a refund of the tax that was incorrectly withheld. You should also fill out Form REV-419 and give it to your employer so that they stop withholding Pennsylvania income tax.

If you had self-employment income from PA, or any other PA income besides a W-2, then you would file a PA nonresident tax return to pay PA tax on the income, and you can claim the credit for tax paid to another jurisdiction on your NJ resident tax return. For more details about the NJ credit see New Jersey Bulletin GIT-3W. The following is a short excerpt from that bulletin.

"This credit minimizes double taxation of income that is already taxed by other jurisdictions. Though the credit reduces your New Jersey Income Tax, you are not necessarily entitled to a dollar-for-dollar credit for the total amount of taxes paid to the other jurisdiction. The credit represents the amount of New Jersey Income Tax that you would have paid had the income been earned in New Jersey, or the amount of tax actually paid to the other jurisdiction, whichever is less."