both are a bit confused. They started out, in intent, as synonymous, but then some craft brewers started to get large enough to make the appellation 'microbrewery' ridiculous. Now, a microbrewery is a small brewery. How small depends a bit on opinion. I believe I've heard it opined that it means a brewery producing less than 12,000 barrels of beer per annum. Most microbreweries are craft breweries, but don't have to be.
'Craft brewery' is even more loaded. Randy Mosher's definition is that a beer is a 'craft beer' if a homebrewer (current or former) gets to decide what it tastes like. That is, quality and not cost or efficiency is the primary motivation. Sometimes it's a bit of a fuzzy line.
Basically, you call a brewery a microbrewery if it's small. You call it a craft brewery if it's trying to make better, more flavorful and interesting beer than the mass-market industry.