Mastered is used interchangeably with completed, in regards to all the categories of jutsu. Specialized is the distinction previously mentioned, where the first category is, of course first specialized, or primarily specialized, and the other is secondarily specialized. This primary specialization gives the ninja the ability to perform jutsu of that category (say, Fire, Water, Genjutsu, etc) with only one handseal. The secondary specialization gives the ninja the ability to perform jutsu of that category with faster handseals, in comparison with other ninja of the same rank.
It is not to be confused with someone claiming to be a Master of something (not mastered, being a Master). That is a title that is only applicable to Taijutsu and, of course, CFS, which is an area of Taijutsu. A Taijutsu Master is someone that has completed all Taijutsu ( Normal + Kaito + Elite Kaito ), while a Taijutsu Specialist is someone who completed Normal Taijutsu. Those are distinguished because they have different attributes in the Speed Chart. For a CFS, the title of Master means the practitioner enjoys bonus attributes as stated within the style's submission. You can only chose one CFS to be a Master of ( be it of your creation or not ) and it must be stated in the bio.
These titles, when not related with what jutsu you learned, can be different in your main bio and secondary bio. You can be specialized in Wind in one bio and Water in the other, it's all pretty flexible.