Some law schools explicitly require a letter of reference from a former instructor (ideally a professor you had and were able to form a close relationship with during your undergrad), otherwise what other posters in this thread have said is correct.
This did send me down a fun rabbit hole of how many SCC Chief Justices each school has contributed during the Court’s history.
The obvious takeaway from my research is that if you want to be the CJ of the SCC, you should: (i) preferably, never go to law school and simply read for the bar; (ii) if (i) is not an option, attend, in order: (a) Laval; (b) Osgoode; (c); Montreal; (d) McGill (e) Manitoba; (f) Alberta; (g) Ottawa.
Since past performance is obviously predictive of future success, I think the only logical thing to do with this information is take it as incontrovertible proof of distinctions between law schools and to adopt the above as a comprehensive ranking of Canadian law schools.
We should also consider disbanding U of T’s law school, seeing as it charges so much money while offering a literally zero percent chance of ever becoming the CJ of the SCC.
[More seriously, it actually was interesting to learn about which schools have produced which justices, though obviously it’s meaningless.]
Based on UBC's phrasing, it seems they only count the credits put towards your degree (for example, if you did college or another program and dropped out, those may not be included). They also drop a certain amount of your lowest classes depending on if you apply with 3 or 4 years under your belt. Best of luck to you!