I think you've answered your own question.
The first type of mount is for screwing into a stud, the second is for drywall/plasterboard.
You can still use the first type though.
Cut the hole for the switch in the drywall and then cut a length of batten just longer that the hole. Then fix this to one side of the hole inside the cavity. This is the tricky bit as you might end up having to screw into the batten through the drywall, which is going to leave you with a couple of screw heads to cover. If you can use an adhesive that should work as the bracket and light switch aren't very heavy.
Once the batten is firmly secured, fix the batten as illustrated on the web page.
However, I would first see if you can arrange an exchange.
There is a ton of information and history out there.
Studs are strong pieces that are the internal structure of your walls. They are covered by some type of material (the "skin") that is what you see when you look at a wall. If you imagine your wall without any type of skin material, there are probably two studs at the left and right edges and definitely two framing members (similar material as studs, but the term studs explicitly refers to the vertical members) going horizontally at the floor and ceiling forming a rectangle. This rectangle has many vertical studs inside of it, usually space at 16" or 24".
A term you'll see sometimes is 16" O.C. which means On Center; it just means the center-line between two studs is 16" apart and there is about 15.25" of air in between them.
Your studs are covered on both sides by something. These days it is typically drywall (sheetrock) which is cheaper and easier to install than most alternatives. Your surface could also be plaster, paneling, tile, etc.
You need to use a stud finder to locate where your studs are because you need to attach heavy objects to studs. Drywall can only support very little weight. To use a stud finder:
- Put masking tape horizontally on your wall.
- Place the stud finder against the wall, holding it vertical.
- Press and hold the button.
- Hold it still for the first half second so it can calibrate itself.
- Move the stud finder horizontally across the wall and mark on the tape where the signal is strong.
- If the signal acts weird, make sure you slide the stud finder sideways at the same height.
- Take a tape measure and try to find a pattern between your marks that is 16" or 24" apart.
- Now you can measure multiples of 16" or 24" and know where other studs are.
You need to determine if your stud are wood or steel because the type of fasteners (screws) you use depend on it.
There are other methods of determining this, but here's one: Figure out where your fasteners are going to go and drill a small pilot hole (smaller than the size of the fastener). If you get about a 1/2" deep and hear a terrible screeching noise followed by your drill bit sliding and having no resistance, you have steel studs. If you get 1" in and you start to see saw dust coming out of your pilot hole and your drill still feels like it's biting at something, you have wood studs.
If you have wood studs, you can use general construction screws (NOT drywall screws). If they are steel, you probably have to use toggle bolts. Toggle bolts are a pain to use, so you can try using self-tapping machine screws with a fine thread first. Make sure your fasteners are long enough.
There are many other types of walls out there so if things don't seem right, maybe they're not typical stud walls.
Best Answer
Typically the studs would be fastened to the wall with clips or L metal. Spacing would be 24 inches vertical & 48 inches Horizontally. Metal studs have a punch out for bridging typical 4' 6" vertical for cold rolled channel to be in stalled some bridging require clips screw attached and others just snap in place depending on the manufacture. You also need to check on the Seismic rating as you stated plaster was being installed.