What is the exact difference between those two words an especially when can пожелание be used and the other one not?
"желание" is wish, desire in a sense that you usually asssociate with the word: something you want to happen/to have. When a djihn or a fairy grants a wish, it is usually "желание".
"Пожелание" is something you wish someone. Also a very popular word for suggestions ,request, wish, often for improvements (a stock phrase "ваши пожелания" ~ "any suggestions?"):
- Наши наилучшие пожелания! = Our best wishes!
- Они учли наши пожелания относительно длины текста ~ They have taken our wishes/suggestions concerning the length of the text into account.