Correct.
These are all equivalent medical degrees
BMed=MBBS=BMBS=MD (USA)=MDCM (Canada)=MBChB=MB
These are equivalent degrees in Human Biology, Biology, health/medical science
BSc = BMedSc = BS (US) = BHB (NZ) = BHSc
None of BMedSc, BSc, or BHSc are equivalent. Many aussie universities offer all 3. why would they if they were all equivalent? You can study similar things in all 3, but you don't have to.
For example, at Sydney, the BHSc requires 2 majors, the health science major and a 2nd related major. The health science major is not something offered in any BSc, and the 2nd major can be in sociology, which would not be a BSc major.
Also, within a BSc, you can major in computer science, physics, etc, which you cannot do any either the BHSc or BMedSc. The BMedSc doesnt even have majors. The BMedSc at Sydney prescribes all 1st and 2nd year subjects (i.e. there are no electives in these years). In the 3rd years, you must take at least 6 final year medical science subjects, which happen to be the same subjects offered for the related BSc majors (biochemistry, histology, pathology, anatomy, etc.). However, all 1st and 2nd year subjects are distinct from those offered to BSc students. They are resitricted only to BMedSc students. A BSc major requires only two 2nd year and four final year major courses, wheras the BMedSc requires 8 prescribed at 2nd year and 6 electives at 3rd year. Thus, the BMedSc requirements are more rigourous than those of the BSc, though you can choose to take more rigourous subjects than required in the BSc. Also, entrance to BMedSc is much more competitive than BSc. pretty much anyone can get into to BSc, but the BMedSc will require you are a demostrable good student.
the 3 are not equivalent. however, they are similar to a N. American BS, in that they are science related undergrad bachelor degrees.