The language used can be very confusing. All states have a "permanent" or "full" license, which is the license that most practicing physicians will have.
All states that I know of have some sort of "temporary" license. This is a full license that's only good for a few weeks/months, designed to be used if you are coming to that state to work over a summer, or as an academic physician for a short period of time. They are much eaiser to get --- basically if you have a full license in another state, you can get a temporary license.
Last, some states have a "limited" or "training" license. This is what residents have, and specifically requires ongoing supervision in a training program. Not all states have such a category.
The link you've posted above is something new to me. Before showing me the link, I would have told you that this doesn't exist anywhere. If I'm reading this correctly, this is a license that any ECFMG physician can get, without any residency experience. You can only work under the supervision of another licensed physician, and can only do so in very specific locales -- Nursing home, psych hospital, chronic home for the ill, etc. Although you can use this license in a "general hospital", that does require GME training (the same for a full license, so I don't see any difference there). It's only good for 2 years, and you can only renew it if you can demonstrate that you're moving towards full licensure.
Looking at this, it seems the only real use for this visa is for a physician that has completed residency training and needs a licensce, but is not a US citizen or PR. Looks like in NY, you need to be a citizen/PR to get a license. There does seem to be some wiggle room in the regs, and I have no experience with this, so could be wrong. But, if a physician on an H whom was working towards a PR wanted a license in NY, they could definitely get a Limited Permit, and then transition to a full license once they have their PR.
I guess it could also be used by a US citizen who fails Step 3, and wants a license while trying to pass Step 3. That sounds crazy -- it would be quicker to just take Step 3 again and pass. But if someone were having trouble passing Step 3, or if they end up not meeting the 7 year rule and need to retake earlier steps, then this might be a reasonable option to allow you to work while you address those things.
Whether anyone will really let you work on this is another issue.
I doubt you're going to find this type of license in many other states.