Wall brackets can be used with all styles of shelving and are needed to support the front lip of the shelving where ever side walls are available.
The only case where they are not needed is if you are using 12" deep SuperSlide shelving and have a hang bar attached, in which case you will use 980 - SuperSlide wall brackets. They are also not needed if you are using the ShelfTrack system, if you are installing shoe racks or if you do not have a side wall to attach to.
If you do not have a side wall to attach to, you should use either 1009 - Shelf support pole, or 1164/1166/1180 - Shelf support brackets.
The wall brackets are sold separately and come with all screws and anchors needed. They will work with both solid and stud walls.