I have a very clear definition and difference between Dominant and Master, though, it is a bit different from any here.
First off, the way I see it, being a Dominant or a submissive is a natural thing. Even in the everyday vanilla world there are those that are dominant and those that are submissive. And, often times, as human behavior would have it, we have the potential to be both, depending on our circumstances. For instance, a man that is Dominant in the bedroom may very well be submissive in the company of his employer. We do choose one or the other out of natural survival instinct, however, it is also natural for their to be a heiarchy of dominance. Males in nature are mostly dominant, women are mostly submissive, and castrated or weaker males usually rank even lower than women because they have little or no use and therefore are extremely submissive being seen as even the weaker sex than women. And, in BDSM, often times, this heiarchy remains.
Okay, so how does all of this add up sexually and in BDSM? Well, a Dominant, for me, is a man that chooses to use his natural sexual dominant place during his sexual experiences. Being a Dominant, in my eyes, is simply being on "top" of things, being on the taking end rather than the giving end. (A submissive would be on the giving end.) If you are in a D/s relationship, it is much like dating. You can be very casual about it or you can be very serious about it. But, there is no vow of commitment between the Dominant or submissive. It is much like dating. Yes, there are several people that date seriously and monogamously, there are several people that even get engaged while dating. However, it is still not a marriage of total commitment.
Being a Master is like being a husband. There is TOTAL and COMPLETE commitment. (Or should be.) Many can be a "Dominant" (or a boyfriend) but very few can rise up to the challenge, commitment and responsibility of being a "Master" (or a husband). When you are a Dominant (or a submissive) you still have certain freedoms. You are truly and honestly in it for YOU (when it comes down to it) and it is rather easy to walk away from. When you are a Master (or a slave) in a M/s relationship you are in it for the both of you. You have made the commitment, you have exchanged the vows, you have a responsibility to the other person now and it isn't just for you. And, it is a whole lot more difficult to "walk away" (or at least should be).
You can say you are a Master or a dominant but it is your actions and level of commitment, knowledge and wisdom that make you one or the other.