The CA is two-dimensional, and follows several simple rules. If the surrounding 8 squares have more than 3 or less than 2 cells occupied, then a living cell will die. If there are exactly three cells alive around a dead cell another cell is born.
Genetic algorithms use basic principles of biology and evolution to breed solutions to a problem.
A problem is encoded in such a way that it can be represented as a vector. A population of random vectors is created and tested on the problem, after which a fitness is assigned to each of the vectors in the population. Normally then, the most fit vectors are breed together to create the next population. GAs are essentially search algorithms, searching for a solution is a very large problem space. See the Generation5 essays .