The difference is obvious instead of finding the non-dominated front of the created offspring population only, in NSGA-II Parents and offspring are combined to form one set of size 2N. Then a non-dominated sorting is used to to classify the entire population.  a  new population is created from different fronts . The crowding distance (based on sorting the values of many objective functions) is calculated to get an estimate of the density of solutions surrounding a particular solution i in the population.

The crowding distance and ranking is used in the tournament selection for reproduction instead of using fitness only.

The advantage of using NSGA-II is no extra niching parameter is reuired. But, the disadvantage is when the latter generations, when more than N members belong to the first non-dominated set in the combined parent-offspring population, some packed Pareto- optimal solutions may give their places to other non-dominated yet non-Pareto-optimal solutions.

Dear Matthieu, it happens that at each evolutionary generation a set of non-dominated solutions regarding the current population is obtained but these solutions may not be in the true Pareto optimal set.

Yes Matthieu. 

http://www.sciencedirect.com/science/article/pii/S1568494606000809

This formulation of the crowding distance presents an instability in the produced results when the front F includes some individuals sharing the same fitness. 

Assuming an unstable sort, the crowding distance assigned to individuals sharing the same fitness can vary between calculations Most implementations, including Deb's reference implemen ation, use an unstable quicksort to sort the individuals