That is one of the problem : many States have different phraseogies and rules regarding this. . However both your examples indicate that using the term " Fuel minimum " will not give you any priority or assistance from ATC . In fact in some States you will get no reaction .
ICAO PANS OPS states it quite clearly . So, if you expect priortity from ATC , use MAYDAY .
( for those who want to know more may I suggest you visit the (excellent) Skybrary.aero site and type "Fuel emergencies , advice to controllers " in the search box )