A/B testing is a catch-all term for multi-variant experimentation. Multi-armed bandit is a specific approach to testing[1], and even though most frameworks provide A/B/N testing -- that is, not necessarily just two variants -- it is easier to say 'A/B' instead of 'A/B/N'.

http://analytics.blogspot.ca/2013/01/multi-armed-bandit-expe...