Sorry for the delay in getting back to you. I’ve had a look at the videos and it seems they’re just not using the correct English terms for these parts.
You’re actually after:
Screw sizes are a bit complex! There’s an awful lot of engineering that goes into the humble screw!
The Arduino Screw size is read as a “Number four by one-quarter inch long, self-tapping screw”.
The Gripper Screws are read as “Two dash fifty-six by three-quarter inch long machine screws”, while the Gripper nut size is read as “two dash fifty-six nut, three-sixteenths of an inch across the flats, by one-sixteenth of an inch thick”.
These are US (Imperial) sizes, whereas most other countries in the world tend to use Metric sized fasteners (although Imperial fasteners are still quite widely available.
Breaking it down:
“#4” and “2-” are the nominal diameter of the screw ie. the name of that size of screw. It’s roughly the same as the real physical diameter, but when you get down to the nitty-gritty you’ll find there are quite a few different diameters of different parts of a screw and its nut.
Number sizes are very small imperial sizes. There are mathematical formulae used to determine all the dimensions of a Number size screw, and the name Number comes from the number used in the formulae.
Confusingly, these are also known and sold as Gauge sizes (G) - but this is actually incorrect as gauge is something else, related to wire drawing, and the sizing works in the opposite direction (where a higher number means the wire was drawn through more gauges and is therefore a smaller size).
Dash sizes are the next smallest imperial size of screw. Dash sizes are the diameter of the screw (or other part) in 16ths of an inch, so a 2 dash screw is 2/16" = 1/8" (note that " means inches).
The “56” is the thread count, and refers to how many threads per inch (TPI) there are on the screw. Metric standards usually use the actual distance (or pitch) between two threads instead (eg. 1.5mm).
The length of a screw is measured from the fastening suface:
Tapping is the act of cutting a female thread (Bolts have male threads, nuts have female threads). A self-tapping screw is one that cuts a thread into the workpiece as you install it.
A machine screw generally refers to a bolt like threaded fastener, which conforms to either the UN, BSW, or ISO thread standards used on bolts, but is entirely threaded, unlike a bolt which usually has an unthreaded portion of the shank (particularly the case for longer bolts).
Finally, AF (or Across the Flats) refers to the distance between two opposing flat surfaces:
Thick refers to the dimension m in the diagram above. A stanard 2-56 UNC Hex Nut is 1/16" thick, so it’s not usually specified unless it’s important to the application (critical applications may require more back-up threads, or other specialty nuts such as Nyloc anti-vibration nuts may have different dimensions).
I’m glad my degree was at least a little bit useful!
Here’s a really good resource: https://www.boltdepot.com/fastener-information/Measuring/Notation.aspx