kalk (calcium hydroxide) add calcium and maintain alkalinity by adding OH- ions to your system. by doing so , your PH will be raise too.
CR ( calcium carbonate) add calcium and maintain alkalinity by adding carbonate ions to your system. by doing so, the amount of buffering agent will be increase in your system. Thus, ur pH will not flatuate and be stable .
pH is defined by the concentration of OH- ( hydroxide) ions in your system, something like negative log the concentration of hydroxide ion in standard unit.
alkalinity is defined as the concentration hydroxide , bicarbonate, carbonate in your system.
pardon me if my defination is not accurate enouggh, chemistry is such headache during secondary school.
however CR need a CO2( i think carbonic acid will be produce) as it require low pH to burn the calcium carbonate to release the calcium and carbonate .