These types complement each other, as will be described below. Professions generally fall into one of three types, although there is overlap. † With Legion, this is not quite true as there are purchasable 'catchup' items ( Forgotten Tomes of the Broken Isles) to re-learn all Legion expansion recipes previously learned.
Engineering and the secondary professions tend more towards allowing you to enhance or otherwise help yourself, and not so much benefit others, but it is possible to make money from them as well.
Most primary professions have capabilities that other characters need. Every character can learn any or all of the secondary professions. All of your progress in the forgotten profession will be lost † and your decision will not be undone if you change your mind, so be sure you want to change. If you want to learn a different primary profession after you have learned two, you can unlearn one or both of the ones you know. Every character can have up to two primary professions at a time. Professions are either primary professions or secondary professions.