Regarding the U.S. (I think that, in Canada, Quebec has different degree titles and is exempt from this discussion)

M.Arch. (2 year) allows one to register in all jurisdictions, if NAAB accredited.

M.Arch. (3+ year) allows one to register in all jurisdictions, if NAAB accredited.

M.Arch. (1 year) is meant for B.Arch. or professional degree holders, and it is the preceding accredited professional degree that allows one to register.  These degree programs are not accredited.

M.S.Arch. (around 1 year) is somewhat like a M.Arch. (1 year) in that it focuses on a specialty area, and usually for those with an accredited degree.  They are not accredited. However, adding an M.S.Arch. to a non accredited BA/BS in architecture (in the U.S.) will mean that none of your architectural educational pursuits lead to registration possibilities in all jurisdictions.

Msc in architecture is not professionally qualifying. It is typically a postgraduate degree focusing on a specific domain (for instance sustainibility, theory, digital based...etc) Be also aware that there is also the MArch II (2) that is also postgraduate and non professional. It designates a course of advanced design and would be, unlike the course led Msc, project based. Always good to check the specifics of the degree on the university website and with the university.