First off Dave I have looked at the two links you have posted and whilst technically correct they are far too complex. They discuss parts of gears and formulae that the average Joe Bloggs has no control over.
So to basics. Gears are measured by their Diametrical Pitch or DP for short. This is the imperial standard just like threads are measured in TPI It means how many teeth on a pitch circle. The pitch circle is a theoretical circle about 1/2 way down the teeth, imagine two smooth rollers running together, that's the pitch circle
Great store is place on the DP but as it's hard to measure we work on the Outside Diameter, OD, which is easier. If the OD was the pitch circle it would have two extra teeth on it - fact. so from that we can work out what the DP is.
Example: We have a gear of 2.100" OD and 40 teeth so we add 2 to 40 to get 42 and divide the OD into that and we get 20. So this range of gears is called 20 DP.
We now need to find a cutter to make this gear. From tables in Machinery Handbook, various gear books, the net and last Octobers issue of Exchange and Mart we find that there are 8 cutters required to make a set. This is because as the pitch circle diminishes the teeth take on more of a curved shape. In actual fact every number of teeth is different but to save on tooling they have been fitted into 8 bands. In this case cutter number 6 will cut from 17 to 20 teeth.
So now we have the DP, the OD and know what cutter.
On the cutter should be various markings like 20 DP, 14-1/2PA and D+f = 0.108" We know what the DP means and we will deal with the Pressure Angle, PA, in a moment so that just leaves D+f which stands for depth , D, plus clearance, f,
At this point we have all we need to cut a 20 tooth gear. No fancy formulae and because the makers of the cutter have done their homework we don't have to worry about all that mumbo jumbo of Addendum ,Dedendium Ear of Bat, Tongue of Newt, etc, etc.
So we mount our blank of 2.1" in diameter on a dividing head or some for of indexer that can do 20 divisions. The cutter is brought central on top of the work, or the side if using a turret mill and just touched onto the work. Now we wind clear, feed in 0.108" deep and cut one tooth. wind clear, index round 1/20 of a turn and cut the next tooth. carry on until done.
And that's it in basics.
Pressure angle is usually in two forms14-1/2 degrees and 20 degrees.Quite hard to measure as the differences are so small but rule of thumb is if it's pre war in origin it's 14-1/2 and post war usually
20 degree's. Most lathe change wheels are 14-1/2.