Not anymore. Opiates like morphine and codeine are still derived from the poppy plant, but now that scientists have learned how to synthesize opiates there are many that aren't directly from the poppy plant. Heroin, for example, is considered semi-synthetic--it is synthesized from morphine, which is derived from the poppy plant. Others are completely synthetic, like fentanyl and methadone. These aren't made from the poppy plant.
There are many more synthetic opioids than natural ones, but a lot of the opioids currently used to treat pain are poppy-based: codeine, morphine, heroin, hydrocodone, oxycodone.
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