I think most are in brain, Kappa is related I think to spinal anaesthesia such as epiduralOpiates are morphine and its derivatives like heroin, codeine, buprenorphine etc. They all have the same opiate skeleton and the difference is which extra chemical groups are bolted on the edges.
Opioids are drugs that produce similar effects but may not be related to morphine. Tramadol and fentanyl are the classic examples.
Almost all drugs work because they fit into receptors in the body like a key into a lock. Opiates (through a combination of size, shape, charge and hydrophilic/phobic interactions) fit into the opioid receptors and trigger an effect. Synthetic opioids can trigger those receptors (fentanyl has basically been designed to do that as efficiently as possible) but may trigger other receptors as well with consequent side effects. Tramadol's potential side effect of hallucinating large hairy spiders is one example.
Jarrod has already mentioned the three opioid receptors I know (mu, kappa and delta). I can't remember which ones do what in particular but they are all similar. The opioid receptors control a number of bodily functions but the main one people care about is pain. Trigger enough opioid receptors and pain signals are still generated but the brain essentially ignores them.