Both numbers mean the same thing so the one you use depends on what you are trying to do. If you are trying to calculate RA, for example, the formula is
RA = alkalinity - [calcium_hardness + magnesium_hardness/2]/3.5.
If you want RA in ppm as CaCO3 (the more usual way of expressing it) then calcium_hardness (and the other terms) should all be in ppm as CaCO3 as well. If you only had the as Calcium number you would have to convert that to as CaCO3 (by dividing by 20 and multiplying by 50).
The popular spreadsheets want mg/L as the ion (i.e. not ppm as CaCO3). Fancier ones let you enter in any units (mg/L as the element, ppm as CaCO3 or mEq/L) and use radio buttons for you to specify which.
Some water authorities report calcium and magnesium in terms of hardness (ppm as CaCO3) and some as the ion (mg/L Calcium) and some give the numbers in both sets of units. Ward Labs, the source from which most homebrewers derive their water information, reports these as the ion but reports alkalinity as CaCO3. You need to understand what units your data are in and what units you application requires and know how to convert.
Finally, as it is the subject of another thread here, there are approximately a million mg of water in a liter (depending on temperature and concentration of dissolved items) so that 1 ppm is approximately 1 mg/L