Ok AEGD=advanced education in general dentistry
GPR=general practice residency
Aegd is university based that means you are a resident in the dental school. You do general dentistry treatments. You also get referrals/ consults from the undergrad students and you work with or refer to other postgrad specialties such as perio, prosth, endo,omfs...etc
Gpr is the same but hospital based that means you are a resident in the hospital which means more exposure to compromised patients.
You receive a certificate and you are considered a general dentist with more experience and training but not a specialist. They will make your application stronger if you apply to a specialty.
As for applications, check ada.org it has a list of all programs. Check their requirements and apply.
Aegd/gpr don't make you a licensed dentist but it qualifies you to take the license exam and they don't give you an undergrad DDS certificate.
Hope this helps good luck