Here's what happens if you want to move to a "different place".

Say, you go to a different country: you have to spend upwards from a few month, but likely few years to confirm your degree. You won't need a stage, but you will not become an attending right away. In many cases there aren't even analogous positions if you move countries, unless medical systems are very similar, so, in most likelihood you will have to do at least a good chunk of residency training all over again. This will also be usually compounded by studying a new language to a very high degree as doctors are expected to produce a lot of written reports / engage in written communication, and, unlike programmers who almost universally use English regardless of the country they work in, doctors absolutely have to have good command of the local language(s).

Similarly, if you move between different medical organizations which manage hospitals. Sans the language requirements. However, within the same country hospitals will usually be more similar than between countries. Anyways, most hospitals will have fixed dates when job applications are processed, and even if you are extremely lucky and you don't need to redo any of your previous residency (both systems use the same PACS system, same or very similar internal organization etc.) you will still have to wait until the "draft" date. Typically, and due to competition, doctors will go to the hospital they intend to work at anyways before the "draft" date.

Even within the same hospital, if you want to move to a different department, you will still do residency, at least in part. I.e. say, you were already an attending in internal medicine, and you want to move to radiology: then maybe instead of 4 years, you'll do 3 years residency.

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The above has a lot of compounding factors. Huge waiting times to get a position lead to doctors holding on to their positions with a lot more devotion than programmers. In many cases it's a job for life.

Because hospitals have to be in geographically diverse areas, they cannot, like programmers, all bunch together in one or two cities in a country and jump jobs w/o moving to a different apartment / house. A lot of hospitals thus include accommodation programs, which make it even harder to switch jobs.

It's very common for doctors to marry doctors. This makes some things easier, but it also means that if you need to switch jobs, then you have to do it in lockstep with your spouse.

Not in the least, if you move from a "less prestigious" country to a "more prestigious" country, you are almost automatically downgraded in your rank, and if you want the equivalent job, you'll have to jump through the same hoops the second time.