Is Hydocone and morphine in the same drug category?

Basically, yes. Percocet is a combination of oxycodone hydrochloride and acetaminophen (Tylenol™). Morphine, like oxycodone, is in the opioid family.

Addition by Echo646: Morphine is stronger than percocet, however, and it can be more addictive and more likely to cause dependence, so even more care should be used when taking morphine. Every other opioid is judged by how well they treat pain compared to morphine.