No, physical dependence is most definitely not addiction. This is a very common misconception, one that even many doctors believe.
Take for example a chronic pain patient who has been taking opioids for an extended period of time to manage their pain. They take it exactly as prescribed, do not get high, never run out of medication early, and do not constantly ask for a higher dose (unless their condition worsens or because of tolerance). They take opioids because it treats their severe pain well enough for them to lead a normal life and to be able to work full-time.
These patients of course have developed a physical dependence on the opioids, and if the underlying cause of their pain is cured, they will need to taper down their dosage to avoid physical withdrawal symptoms.
But they are certainly not all addicted to opioids.