Both NY and NJ are “One Party Consent States,” meaning that as long as you have the consent of one person who is party to a communication (or if you yourself are party to the communication), it is legal for you to record (or “intercept”) said communication.
However, NJ specifies that just because you own the phone that you own, you cannot record a conversation unless you are on the call or a party to the call gave prior consent to make the recording.
It is illegal in both NY and NJ to own a device that is primarily used to intercept or eavesdrop on calls or other communications. An audio, video, or other type of recording application on your phone, for example, would not be illegal, as the primary purpose of your phone is not to record communications. Conversely, a “bug” used to tap someone’s phone would be illegal, as the only purpose of the bug is to intercept private calls.
Likewise, in both states recordings are admissible into evidence during trial so long as the recording was not made illegally.
You also cannot use the recording to commit a crime.
More details on the legality of recording communications in New Jersey and New York can be found in N.J.S.A 2A:156A-4(d) and N.Y. PEN. LAW §250, respectively.