If you look at a potentiometer (pot for short), you will notice a shaft coming out of it which is where the manufacturer installs a knob to control the pot. A control shaft usually has a certain number of splines (or ridges) around its circumference. This number will dictate what knob will perfectly fit on it.
There are three common types, coarse, fine, and solid shaft.
Coarse Splined Control Shafts and Knobs
These are metric in size, which is why they are also known as Metric, or Imported. They are the most popular type of control shafts and are featured on a wide range of popular imported guitars. They feature a 6mm split shaft and have 8 splines on each side of the split, making a total of 16 on the pot. However, to account for the split in the control shaft, the guitar knobs have an additional 2 splines, therefore totaling 18. This is how they are labeled, so if you have an imported guitar, you will probably need an 18-spline knob.
Fine Splined Control Shafts and Knobs
These are imperial in size, and include popular US-based brands such as Bourns and CTS. They are 0.235" of an inch in diameter, which is 5.95mm, making them ever so slightly thinner than the metric version, with finer splines. Being smaller in size, they have 10 splines on each side of the control shaft split, making a total of 20. But, once again, the knob that perfectly fits onto the shaft will have additional splines (to make up for the splits in the control shaft), this time making a total of 24. This type of pot is only usually found on higher-end guitars and the potentiometer brand will often be listed in the product description, guaranteeing quality.
The above-mentioned 2 shafts are split shaft control. There's still solid shaft control.
Solid Shaft Control Shafts and Knobs
And finally, we have the solid shaft, which has no splines and features a smooth, ridgeless control shaft. It therefore requires a knob with a set screw, which is screwed directly into the control shaft, as opposed to the push-on design of the other two designs. It is an imperial size of a ¼ of an inch in diameter or 6.35mm, making it the largest of the three sizes. Therefore you can only comfortably install a ¼" diameter knob to it because knobs of the first two splined designs will be too small.