While you can look at the stealth aspects of Black Flag in a very straightforward manner, there are a few tips that you may not have realized that will help you improve your stealth abilities.
There are even a few missions that require you to sneak around that result in failure if you're spotted or engage in combat. It may be more difficult in some cases, and in others it may be easier, but you generally get the option of going all out or playing the game like previous incarnations of the series and sneaking around.
Many of the story missions in Assassin's Creed 4: Black Flag give you the option of playing as a hacking, slashing swashbuckler.