Do RGB cubic-coordinate and HSL cylindrical-coordinate systems both support same colors?

Both can present the same colors if you have no limitation in your number system. If it happens that the numeric resolution is limited, for ex. to integers only, both systems present a little different set of points in RGB color space.

It can also happen that your computer system can produce different color just for each possible RGB combination and it’s controlled by sending RGB combinations. If you have only integer values 0…255 for R,G and B but you can input HSL numbers with steps say 0,1 degrees for Hue and say 0…100% with 0,1% steps for S and L then some HSL combinations maybe cannot be shown in your system. HSL has more possible color combinations as numbers, but not all of them can be shown as different colors. Many HSL combinations are rounded to the same RGB combination.

Find conversion formulas and calculate with math or test with a color system conversion calculator how much say RGB numbers must change to get the minimum possible change in HSL system.

An example:

That’s pure max bright green RGB(0,255,0) You must insert 3 units blue i.e. to RGB(0,255,3) before the hue grows one degree – from 120 dgrees to 121 degrees. If you can use only integers as your hue angle you cannot input RGB(0,255,1) nor RGB(0,255,2) as HSL numbers.

The used calculator was https://www.rapidtables.com/convert/color/rgb-to-hsl.html

It has also conversion formulas.