There are many ways of spelling the name of this game - Kalookie and Kalooki are common alternatives - and these names are used in different places for more than one type of rummy game.
In some countries Kaluki is a basic two pack rummy game with 13 or 15 cards dealt per player and a minimum number of points required for an initial meld. I have seen descriptions of this type from Britain, Sweden and North America, and I have been told that it is also popular in Greece. This type of game is described on the page on Kaluki in Europe and North America.
In some countries, the name Kaluki refers to a kind of Contract Rummy, but the details differ considerably from place to place. Descriptions of two different Kaluki games of this sort are given on the pages on Caribbean Kalooki and South African Kalookie