Is there an equivalent in another country of the French "CIFRE"? A &quot;CIFRE&quot; in French is another type of doctorate where the French government helps to fund a company to hire a doctorand.
There are several differences between a CIFRE and a &quot;doctorat&quot; in France, or PhD, as far as I know, the main are more are less those following:

You are hired within both a company and a laboratory for a CIFRE instead of only a single laboratory for a &quot;doctorat&quot;
You are generally better paid with a CIFRE, slightly more than a &quot;doctorat&quot; but still less than a regular position within a company as an engineer for instance
You are suppose to do more theoretical and less applied work for a &quot;doctorat&quot;, CIFRE aiming to apply your researches for the company that hires you. Also meaning you'll probably publish less while doing a CIFRE.
You have to teach within universities or Engineering/Business schools for a &quot;doctorat&quot; while it's not mandatory for a CIFRE

Here I'm not focusing on doctors of medicine at all (a French distinction exists).
I was wondering if this kind of huge distinction exists in UK or US and if not, in any other country.
Yes. 

CIFRE is a mechanism for PhD students in France to be funded and work with industry.

The US NSF offers similar opportunities through the Non-Academic Research Internships for Graduate Students (INTERN) Supplemental Funding Opportunity.