Merriam-Webster's dictionary dates mixology to 1948 and defines it as:
"the art or skill of preparing mixed drinks"
Mixology has become a more common used term in recent years and is generally accepted to be a refined, higher study of mixing cocktails and drinks than the everyday actions of bartender. This definition and it's use is one of much debate in the bartending community, usually because of the impression it leaves that a mixologist is better and more skilled than a bartender. This isn't necessarily so. Neither is "better" than the other and each require a different set of skills, but then again the two titles can be interchanged.
A bartender needs to have a variety of skills which are highly important and some that the mixologist may not develop or use on a regular basis. In general a bartender needs to know a lot of common and popular cocktails, serve many people at once, think quick and be the ultimate people person. The mixologist tends to focus on the art and craft of mixing cocktails, studying the classics, concocting new and exotic drinks, experimenting with lesser known distilled spirits and mixers, and, overall, pushing the limits of classic bartending.
Again, these distinctions are the generally accepted differences between the two roles and are meant for clarification. In my view, if you want to be called a bartender, do it and if you want to be known as a mixologist, you're just as free to do so.