Pennsylvania, New York and New Jersey are all part of a Driver License Compact (DLC) that allows for the member states to report tickets received by motorist back to the state where the license was issued. Each state that takes part in the DLC can have its own rules about how they put this information onto your record or assess points for out of state tickets.
Pennsylvania has decided that even though minor traffic offenses such as speeding, running red lights, etc are reported to to Penn DOT, that these offenses will not appear on your PA driving record. So unless your New York speeding ticket was considered a major traffic offense it does not likely appear on your PA driver's license.
Now when moving and becoming a resident of a different state and obtaining a new driver's license, many states do not transfer points from your old state over to your new license. They will normally check to make sure that any old violations were properly taken care of though before issuing a new license.
For insurance purposes, points from your old license can be seen because if you recently moved to a new state many insurance companies will also check your driving record in your former state. If you have more questions regarding your driving record in PA or your new license in NJ, you can contact the state's Departments of Motor Vehicles.