Depends on whether it is economy, business or first you are flying + whether it is domestic or international.
The higher of the two (sts vs class of flying) will be applicable:
For a SG I believe the following applies:
DOM - Y class: Priority Tags
DOM - D Class: Buss Tags
INT - Y Class: Priority Tags
INT - D Class: Buss Tags
INT - F Class: First Tags
More so than just following the "rules" it highly depends on who is behind the check-inn counter. Buss/Prio are often random; First Tags only when WP or flying F.
Still lots of non-tagged luggage on DOM/INT and both Prio and Buss Tags still come out first (in most cases

)