Not every credential has an equivalent in every country, and as far as I can tell, the certificat as you describe it has no direct analogue in the United States. As such, you might find more practical answers at one of our sister sites, The Workplace SE or Academia SE, which answer many questions about listing international credentials and what to put on your CV.
Since there is no direct equivalent, the "best" term for you to use is arguably a matter of opinion; you could use diploma and then hope for a chance to explain what it means to an interviewer, or you might use certificate so that it shows up résumé searches more readily.
In the U.S., academic credentials are not regulated by the government directly, but by various private accreditation bodies; for example, Harvard University is accredited by the New England Association of Schools and Colleges. A degree is a recognition of scholastic achievement granted by an educational institution, and generally accepted if the institution issuing it is accredited. Your diploma is the physical document which recognizes this attainment; the first AHD definition for diploma gives
A document issued by an educational institution, such as a university, testifying that the recipient has earned a degree or has successfully completed a particular course of study.
To say you have received a diploma in a subject (I earned my diploma in chemistry in 2006) implies that you have earned a baccalaureate or advanced degree in that subject. If you do not specify a discipline, depending on context, it may be assumed you are speaking generally of a postsecondary degree, or of your high school diploma, i.e. your secondary school-leaving credential.
Non-degree academic programs, as well as non-academic professional education programs, almost invariably lead to a certificate, which covers a much wider range of attainments.
Certificate is only synonymous with diploma when referring to the physical format of the diploma (archetypically, a piece of parchment or thick paper bearing the graduate's name and the school's seal). Otherwise, I would not consider them interchangeable. Saying you have received a certificate in a subject (I earned my certificate in enterprise document management in 2006) would not be interpreted as saying you have earned a degree in it, merely that you have completed some sort of specialized training course in it. AHD agrees:
- A document issued to a person completing a course of study not leading to a diploma
There is tremendous variability in the nature and quality of various certificate programs, which are proliferating by leaps and bounds. Some are serious university-based courses of study (e.g. an optional Certificate in Health Administration and Policy for University of Chicago Law School students). Some are lengthy training and apprenticeship programs run by standards bodies (e.g. earning your teaching certificate to become a certified teacher in New York). But others lack any kind of intellectual or professional rigor, and can be had for doing little more than paying a fee.