My understanding of the process, as derived from various USyd literature and attendance to their scholarships lecture on Live day:
1) Submit your application and personal statement. They will send you a letter confirming they have received it and are considering you (this is the letter you guys got).
2) They deliver your application to the relevant faculty. You will note that on your application you had to decide what faculty you were applying to. This is because all the scholarships - both the University-wide ones, and the faculty ones - are assessed by specific faculties rather than a central unit. I suppose this is because the Science faculty is best positioned to judge who has the best achievements in science, etc. - Arts people would not be able to differentiate between people who had achieved in science, because they wouldn't understand the various competitions.
3) The faculties decide whether you are worthy of a scholarship. For some faculties, this only involves reviewing your personal statement and submitted school results. For other faculties, such as science, an interview is also part of the selection process. The best candidates are shortlisted for Uni-wide scholarships. Faculties also allocate their own faculty scholarships.
4) When UAIs come out, a check is run on the people in the shortlist to see if they meet the 95+ UAI they need to receive a scholarship. If they do, they get one. The UAI is not used to decide which students get a scholarship - a person who gets 99 has no advantage over someone who gets 96. Also, people who get 99.95 or 100 are also offered a scholarship at this stage.
There is no such thing as scholarships with distinction and credit any more, the two-tiered system was scrapped last year. However, they do give out some things called entry awards which are a lump-sum of $5000 (I think), also requiring a UAI of 95+, for those who just miss out on a scholarship.