The nomenclature can get pretty confusing. Typically speaking though, a Bachelor of Medical Science is a degree completed by those who already have a medical degree, while Biomedical Science is an undergraduate degree that is essentially a glorified/specific science degree that focuses on biology, chemistry, etc. BMedSci is typically one year long (I believe) and revolves around research/a research project.
For all intents and purposes, if you're a high-school leaver, you should only be concerned with degrees to do with Biomedical Science/Biomedicine. However, universities can arguably call the degree whatever they want, so it's best to check on a case-by-case basis. For example, I think there are universities in QLD which have BMedSci degrees which are equivalent to our 3 year Biomedical Science degrees, albeit with a different name. I understand this can be pretty confusing, which is why it's safest to go with the university's description of the course, because names of degrees can change between institutions while the core premise stays the same.
Have a nice day.
@vox: "Weighted" in WAM is simply to do with credit points, I think, not the actual year of completing the units. wGPA (used for med entry) takes into account the year.