BAdvSci is a more 'special' course, and the faculty make special allowances (such as 2nd year research units) to these kids because they are 'special' [high achievers who will do honours and etc]. You have more leeway in terms of customizing your pathway and getting approval for special units and overload and such.
BSciScholar is the special group of the special group, they get a scholarship, more often than not they get hand-picked by professors to undertake research units and they have the option of advancing to honours in two years [compared to 3], and most don't deal with the annoying first year prerequisites, some compulsory crap, and even get permission to do units that require prerequisites they have not met.
BSci is generic, you get treated like crap, unless you piss enough people off or have ridiculously high grades, overloading and special units won't get approved easily.