TCM is the general term for the style of acupuncture which most acupuncturists are trained in, at least initially, and the style which most people practice. As this is the most foundational grouping there is a broad range of techniques used and treatment protocols. Most recent clinical studies regarding acupuncture usually use treatment techniques a/or protocols based on TCM Theory.
Korean Acupuncture is another broad categorization which in actual practice includes some unique techniques and applications as well as techniques and theory from both TCM and Japanese acupuncture. In general there is more use of the Five Element Theory and an emphasis on your body type or constitution when developing treatments. Korean Hand Acupuncture is a popular subset of Korean Acupuncture where the hands are considered a microsystem of the entire body. Within this system you may diagnose and treat conditions anywhere in the body by treating just the hands. This is similar in theory to Auricular acupuncture.
Japanese Acupuncture is a style of acupuncture which requires additional training above and beyond general TCM Theory and Practice. The techniques within Japanese acupuncture are generally aimed at using the least amount of stimulation to create the greatest effect. To contrast with TCM, Japanese acupuncture typically uses thinner needles, less points and less stimulation by using more shallow needle insertions even to the point of just touching the needle to the skin. Additionally, while not entirely unique to Japanese acupuncture, practitioners tend to use the abdomen as a diagnostic tool more often than other styles of acupuncture.
Five Element acupuncture is a speciality practice which can be similar in needling style to Japanese Acupuncture but tends to concentrate more on the psycho-spiritual nature of a person to heal disease - including physical disease. This style of medicine was popularized by the late J.R. Worsley and requires significant training outside of general TCM theory. Most practitioners will have gone to a school that specializes in Five Element acupuncture or at least have done post-graduate study at one.