Is there any difference between these two kind of researchers?
Some physicists teach more mathematics.  Some physicists teach more applications.  It's just a matter of university, teacher, and student preference.  Yes, the way you are taught will influence your career.
I do not think these preferences have anything to do with the country.  A large portion of physicists have experience with multiple countries.  And within a country, you will find quite a range of opinions about how to do things.