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.