In the US, it's called a diploma, or more specifically a high school diploma. Baccalaureate refers to the undergraduate degree granted by a four year college (post-secondary institution). Although, if I recall correctly, my high school had a baccalaureate breakfast just before graduation; I never did really know why.
Typically we use certificate to mean the paper granted by a technical school for completion of a short program (a certificate in auto repair, for example); it's not really considered a degree.
In most school systems in the Commonwealth, when you complete your secondary education, you get a certificate (known variously as the Higher School Certificatein many places in Australia, or the A [advanced] level of the General Certificate of Education). However, even here, some schools offer the International Baccalaureate which pupils take in place of the HSC or A levels - and this is a diploma programme. (I don't know about pop's reference to the Baccalaureate. I know of schools here that offer this in upper secondary school.)
In some U.S. schools, some students participate in the "International Baccalaureate" program, but use of the word "baccalaureate" in the U.S. would strongly suggest the bachelor's degree usually awarded after four years of post-high school study, and would thus be, frankly, fraudulent in reference to a high school diploma.
There are increasing references in the press in the U.S. to high school "degrees," but no actual high school in the U.S. awards degrees. A "degree-granting institution" is a college or university. The references to "high school degrees" are to diplomas.
One circumstance in the U.S. in which "certificate" is used in relation to education at what we call the "high school" level is the GED or General Educational Development test. This is an examination for those who did not attend high school for the full four years or did not graduate and receive a diploma. A satisfactory score on the examination entitles one to a GED certificate which is supposed to be the equivalent of a high school diploma.