An opiate is natural and from the opium poppy plant. Examples of these would be heroine, opium, morphine and codeine. An opioid is a synthetic drug made to mimic the effects of an opiate. These would be Percocet, Fentanyl, Methadone, Oxy, Demerol, etc.
Opiates are said to be more addictive.
As far as your question about receptors....yes there are differences. I used to say opiate and opioids not knowing the difference until I googled "Opiate vs Opioid" a couple years ago. There are actually many difference but at the end of the day....they are all used as a band aid to cover up pain and are all addictive.
Fentanyl is a stonger form of an opioid. Opiate and opioid mean the same thing: Opiate is an adjective while opioid is a noun. Percocet is an opioid as is fentanyl. They are synthetic which means they are man made and not derived from a plant.
Good job on getting off the Percocet!