My understanding is that the difference between fuzz testing and property testing is how the input is crafted. Both can be viewed as a pair of things: a function to generate series of bits as input, and a way to turn these bits into the appropriate data under test.

Property testing generates these bits using a specified distribution, and that's about it. Fuzz testing generates these bits by looking at how the program is executed, and uses a black box to try to explore all paths in the program.

Most libraries for property testing comes with very convenient ways to craft the "input to data" part. Fuzz tools come with an almost magically effective way to craft interesting inputs. The two combines very well (and have been combined in several libraries).