Though the names may vary slightly, and they may be subdivided into more categories, the four basics are Casual (also referred to as Relaxed), Classic, Romantic, and Dramatic (also referred to as Expressive or Trendy). There are descriptions and examples of each category all over the internet (like here and here). There are also quizzes to help you determine which category you tend toward. Some of the quizzes are more "scientific" than others; one includes a question regarding your favorite cocktail (is it more than coincidence that I love martinis and I am a classic with minimalist tendencies?). Unless you have a personal stylist to help you uncover and distill your own fashion personality, I recommend two things. First, take this quiz, just to get an idea which direction you are leaning. Ok, also because its fun. Second, create your personal fashion mood board.
What is a mood board, you say? A mood board is a compilation of images and other elements. These compilations are used in various fields to convey a vision. Interior, graphic, and fashion designers use them to express to clients a "look" or emotion or ambiance that they are hoping to achieve. I propose that you make one with a sort of reverse purpose, that is, with the intent of discovering your look in the board after the fact. So here is how it goes. Ideally, you have a collection of fashion magazines and catalogues that you don't mind cutting up. Grab a bulletin board, some pins, and a pair of scissors (I know you are thinking, "I can do this on Pinterest!" Sure you can, but having a tactile, physical board makes it more real, and put in a prominent place, more easily referenced). Cut out the images that appeal to you. Don't over think it. Be instinctual. Pin the bigger images first and fill in with the smaller images. If you are by yourself, set the board aside until tomorrow. When tomorrow comes, return to it for interpretation. If you are with a friend, ask her to take a look for the initial interpretation (she already has some "distance" because she isn't dealing with herself).
What is the first impression that the board conveys? Do you see the elements of one of the categories emerging? Are there certain styles that appear over and over in various interpretations? For example, I discovered that I really have a thing for man tailored items: button down shirts, blazers, trousers, etc. Also, I found that I do NOT have a "Romantic" bone in my body (so to speak) - there was nary a bit of floral, lace, or ruffle to be found. This method can give you a better idea of what look you love (and therefore chase, consciously or not), especially if you don't exactly fit one of the categories defined above.
I have found that putting a name, however generic, to my personal style, helps me to maintain clarity when I go shopping. I am not as easily sucked in by beautiful marketing and/or beautiful products that just aren't me. I can maintain my balance in a sea of trends, and keep a handle on my style identity through major life changes (i.e. having a baby). I heartily agree with the great Pindar, "Learn what you are, and be such."