a busy place may have few people moving quickly a crowed place may have many people standing still not wanting to go anywhere They can be the same, but as you see it is not always the case.

No, they are not interchangeable, although in many circumstances one might think "crowded' would also imply "busy" when applied to cities. First applied to densely packed group of people, then to things, "crowded" does not at all require the space be enclosed overhead. Example: "The city streets were crowded with people and traffic." (But maybe the parks and buildings were not, and maybe the people and traffic are not moving in activity, so are not "busy."

They are close and usually imply the same meaning. If a city is crowded it is usually very busy.