To get a clear idea let's define both:
Start: This is used to startup a container that was previously stopped for whatever purpose.
for E.g. If you used docker stop CONTAINER_ID to stop a container,all you need to do is to use docker start CONTAINER_ID command to restart the previously stopped container and no data would be lost.
Run: This is used to create completely new containers using an image and then starting them up. You can create multiple replicas of the same image,
This is the command : docker run IMAGE_ID
Hope that helped :)
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