Good info here, and a couple of other notes that might help you understand this mess....

• The registration and the inspection dates are completely independent of each other. If you buy a new car in PA the inspection will expire the same time as the registration, but any other circumstances you have to keep track of that separately. You don't get any kind of reminder of the inspection due date.
• In addition to the registration you'll also have to have proof of insurance for the inspection.