To me, "cycling" sounds more sports-oriented whereas "biking" has a more recreational meaning. In the realm of Fitness though, the terms don't appear to have any major distinctions in their use. I imagine any future questions on this subject will fall into improving technique or performance much like the currently tagged questions do.
I'm in favor of merging the two tags and am leaning more towards merging biking into cycling. I would also throw spinning into this mix even though there are no questions tagged as such.