I have some plasterboard screws like this:
However, without a drill I have a job getting them into the wall. Am I safe to use normal screws on hangings that aren't going to be taking a great deal of weight? In this case it is a rack of coat hooks.
Drywall – What benefit do plasterboard/drywall screws have
drywallscrews
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There are a few possibilities; without knowing more about the layout of the house makes it harder to say for sure.
The internal wall in the garage might be constructed in normal blocks for fire performance reasons. (Without looking, I'm not sure about the fire performance of thermal/lighweight blocks). Also, normal blocks might have been used for structural reasons - for example if the wall is load-bearing (normal blocks generally have a higher compressive strength than thermal/lightweight blocks).
Likewise with the bathroom and en suite - there might be a difference for structural reasons.
Or there might be no firm reason for the difference at all, other than the builders using what they had available - it's not unusual for builders to use what they have as long as it meets any specific requirements for the particular element of the structure.
It's difficult to model the situation with rational analysis, there's too many intangible factors. You could do an empirical test. You need to support 20 lbs per fastener. We can apply a safety factor of 3 for ultimate strength, so the fastener should support 60 lbs without actually breaking. So you would need 2-4 fasteners to support your weight. Round down to the closest whole number. Install the clips as you did in the wall, except now install a metal strap between the screw head and clip. Arrange the straps so you can step into them to weight the system. Arrange the straps such that your weight is distributed evenly to each fastener.
Weight the system and see if they break. If you live in a seismic area, bounce on them a bit and see if they break. You'll either be able to sleep better or you'll know what to do next, depending on the outcome. Obviously there are better ways to set up an empirical test, I chose to illustrate a quick and dirty method just as an example. Be sure you are protected from flying shards of metal.
Regarding an increaser for the number of fasteners. No, you can't do that. It is a valid concept though, for example you can use a higher allowable bending stress in multiple floor joists than you can in a single use situation such as a header. The concept is not generally applied to fasteners.
Response to OP's Update
Shear strength in relation to fasteners partly depends on what the fastener is holding. In this case it's known as a metal side plate condition, meaning the expected failure mode will either be the top of the screw failing through the shank (shear) or the wood collapsing under the compression from the screw. It's rare in reality to have a perfect shear condition, there is usually some bending and tension components as well.
A true shear condition would something like a metal strap screwed to the wood surface and all the force was parallel to the wood surface, exactly perpendicular to the screw shank. In your test, you mostly have the vertical shear component, but there is a tension component as the center of mass is away from the wall surface. We can safely ignore the tension component in calculating a working load since 80# in pure shear is more conservative than 80# shear and, oh... say 15# tension combined.
A picture of the clip was helpful, I imagined a much worse condition. Either way, the ultimate strength will not be proportional to shear alone, there are other factors difficult to model, thus testing is the best approach. The failure mode you experienced is a bending failure, but your actual installation, while having a bending component, is in fact mostly a shear condition.
The duration of load is a factor. The usual allowable stresses specified in construction are for permanently applied loads. The allowable stresses can be increased for shorter durations, 15% for a few months, 25% for a few weeks, 33% for a few minutes. Meaning we should reduce the allowable load determined through short term tests accordingly. But we also don't know the ultimate load since you didn't achieve failure. Just as well, uncontrolled destructive testing can be a little too exciting. You also haven't run multiple tests (I assume) to confirm you are getting consistent results.
Let's say you did run multiple tests and they all actually failed at 80#. When you apply the 3x safety factor, then adjust for duration of load, you end up with a working load of 20#, exactly what you need. Considering there was no failure experienced, and the installation does appear to be predominantly shear, I think your installation is safe. Barely. Next time around, use heavy ordinary wood screws ;)
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Best Answer
There are several approaches to hanging loads on drywall/plasterboard.
Light Duty - The most common anchors for used for light loads are expanding tubes that grip the sides of the hole they are in and flare lightly behind the hole
Others like yours, have a wide thread to grab more surface in the drywall itself. Some of the these threaded anchors have a flaring end, some do not.
The limitation of all of these types is they depend on a small area of drywall to stay solid to hold them. They are good for light loads and when the main force on them is shear force. In a wall application, that means most of the force is pullin down, along the wall (as if you are trying to cut the screw in half right at the wall).
If you put a heavy load on these anchors, there is significant outward force, that is, pulling away from the wall. In a coat rack some of the load is shear (downward) and some is outward. This puts stress on the sides of the hole in the drywall and it crumbles. This is even worse when the load is dynamic (moving) rather than static (non-moving). A hanging coat is static. A coat being pulled form its hook is dynamic. And almost all of that load is outward.
The threaded anchors distribute the load better, but not enough for any significant load. Sometimes this is compensated for by using many anchors. An improvement, but usually not a good solution.
Plastic (or metal equivalent) anchors are almost never suitable for ceiling mounts, where all the load is away from the ceiling surface.
Medium Duty - Anchors for medium duty pull against a larger area behind the drywall to distribute the load.
Expanding anchors go into the hole as a tube and are then expanded behind the hole using a screw, bolt or tool.
There are also toggle type anchors where the expanging section either rotates or springs out to cover a greater area.
The advantages of these anchors is that they spread the load far beyond the hole in the drywal itself. While the hole may be prone to crumbling, these anchors rest on an area of solid drywall, from about 1 to 2 inches around the hole. This gives the anchor much more strength to deal with outward loads of medium duty, as well as shear strength. However heavy outward loads, especially dynamic loads, are pulling on on a few inches of thin plaster and paper. Again, adding many anchors helps spread out the load.
Some of these anchors allow removal and reattachment but some do not (for example, spring toggles fall off in the wall when the bolt is removed).
Heavy Duty - On a plasterboard wall, the heavy duty mounting of choice is directly into framing members.
The most common approach is to find studs, the upright framing members that hold up the wall surface. These are either wood or steel. Screws are driven throught the item to be mounted, through the drywall and into the middle of the stud. An alternative is to screw into cross bracing framing. These are wooden or steel sections running horizontally to brace a wall or serve as a firebreak. These are marginally less strong than upright studs, but for practical purposes can hold all but the heaviest loads.
Studs and cross bracing can be found using a stud finder.
Screws should be long enough to reach at least 1 inch into a wodden stud, longer if the load is especially heavy. In steel studs, finer thread screws should be used (sheet metal screws) and length is less of an issue.
In wooden framing, an alternative to regular screws are hanger bolts that can be threaded into the studs and leave a bolt on the outside of the drywall for hanging the object.
The advantage of hanger bolts is the ability to easily remove and reattach the load using a nut or wingnut.
When there is no framing member in the exact spot needed, it is sometimes worth the trouble to add one. A section of drywall can be removed from the area, a cross brace inserted exactly where you want the mounting and extending horiziontally to the two supporting studs on either side. A drywall patch can be then put back to cover the cross brace (using the drywall section removed or a new piece).