I'm studying digital image processing in university, and now we're doing a work where we have to convert RGB values to HSL, and it has to be equal to the Microsoft Paint. When I finished the implementation I saw that it was not equal to Paint, and searching I found that they don't use [0-360] range, as the usual way to implement it, but [0-240] range.
But even reading it I couldn't got why to do this.
There are several reasons.
We really prefer ranges which have just 256 values. In such case we can store data in a byte. We may use two bytes, but so we will double the memory usage. Or just using more then 8-bits, but so we have to do bit operation on every pixel before doing anything interesting, so very inefficient. Note: with two bytes we can use half-float, which are very useful in some context, but float points are also inefficient on various calculation (but it you do filters and layers composition).
The second reason it is stated in the link you included in the question, but it may need some more information: in many format (especially for video or televisions) we have a limited range (not 0 to 255, but 16 to 235 or 16 to 240). There are few reasons: the analog signal could have more black than black (which may be impossible) and more white then white (realistic). We just calibrated TV so to define white and black points (and possibly broadcaster will filter out the point that are below black. This was useful for some reasons (converting analog data, and more white then white is a colour we experience a lot). With digitalization, TV needed analog to digital converters (and the inverse). These converters costs (and more bit: more costs), and we already used data outside "visible colours" range (in analog signal) for other reasons, outside colours. So instead to have different converted depending on the kind of data (or just more bits on converter), we just keep limited range).
For every colour operation, one should check the range (and the definition of colour space). Quantization may be also a problem (many professional software use floating points, so we are less limited on range (but there are also other reason for floating point, e.g. precision and efficiency when working in linear space [without gamma correction]). Note: you should care only on the ratio value to maximal value. Angles have various measurements: 360 degree, 400 degree, or 2 Pi (the most common, sometime, especially on past you may write then as decimal degree (or other factors, so e.g. 3600, 36000, or 21600 [minutes of degree]). User interfaces may just show a different convention (more convenient for users).
And to make all more complex, the HSL conversion is not so exact, if you want exact H, S, and L (in stricter definition), just a quick shortcut.