A variety of Fasteners are used in theatre construction, but these days screws have replaced most other fasteners. The best are drywall screws and the similar utility and deck screws. These are pointed with sharp threads and heads that self sink themselves in soft materials like pine and fir, although they may break off or strip out in harder materials. Most drywall screws use Phillips head screws because they work well in electric drills. Battery powered drills are most convenient for this. Some shops use square socket (Robertson) screws because they give even better torque than Phillips heads. Screws are sized by number and length, from #2 up to #12, and by the inch fraction diameter above that. The rule of thumb as to appropriate length is to use a screw at least twice as long as the top layer of material you are fastening down.
Very heavy screws with hex heads are called lag screws. They are used where extra strength and holding power is needed, and have a hex head so they can be turned in with a wrench.
Nails used to be the standard fastener, but are much less common because of screws. Nails are usually measured by the penny. A nail penny for common nails was once about the weight of a penny coin, so that a 2 penny nail weighed about the same as 2 pennies, a 10 penny nail weighed about 10 pennies, etc. A more useful way to look at it is that a 6d nail is about 2" long, and for each penny above or below that add or subtract 1/4". A 4d nail is 1 1/2", a 10d nail is 3", etc.
Nails come in different weights.
Common nail: for general construction, with a fairly heavy shaft and a reasonably large head. Suitable for building frames with 2x stock but may split thinner wood unless a pilot hole is drilled first.
Box nail: thinner nail with a slightly smaller head. Don't split thin wood as easily, but because they are thinner they don't hold as well.
Sinker or coated nail: box nail coated with a rosin based glue. Holds as well or better than common nails, while resisting splitting like box nails. Because they are thinner, they do bend easier than common nails.
Finishing nail and casing nail have small but slightly different head for finishing work. The heads are inset below the wood surface to be inconspicuous. They will pull through the wood easily, though.
Duplex nail, also called scaffolding nail or hollywood, is like common nail, but has one head on top of another. When pounded in to the first head, the second head is exposed for pulling nail out easily. Has mostly been replaced by drywall screws.
Staples: come in lightweight wire for lightweight materials like fabric, and heavier wire for wood, plywood, etc. and with narrow crown or wide crown. These last need heavy, usually pneumatic staplers to drive. Staples do not hold very well, so they are usually used with glue to hold wood together until the glue dries.
Where screws will not hold well enough, bolts are used. Bolts are threaded to take a nut as a fastener, and are usually stronger than screws. Bolts come with flat heads, round heads, pan heads, square heads, and hex heads, among others. The most common in the theatre is the carriage bolts, originally meant for building horse-drawn carriages. They have a domed head to avoid catching on things and a square or knurled collar which sinks into the wood so the bolt won't turn. On the other end are the threads for the nut. To keep from having the nut pull into the wood, you need to put a washer between the wood and the nut.
The basic difference between a bolt and a screw are you turn the NUT to tighten a bolt but and you turn the SCREW to tighten a screw.