A fast recovery diode stops conducting quickly when a reverse charge in imposed across it's junction. The quicker the better, as this limits the voltage transient and associated ringing resulting from a change in current across the internal inductance of the diode and it's leads (di/dt). In practice, even with a super fast recovery silicone diode, such as that exhibited by the popular 1N914, a voltage transient will still be created since the recovery event is fast (di/dt again). Our semiconductor industry addresses this by designing a "fast-soft recovery" characteristic into some of their diodes and these have generally garnered wide acceptance. Snubber networks further mitigate the negative effects of di/dt.
A schottky diode incorporates a different junction topology which produces a lower voltage drop associated with it - thus lower power loss and better efficiency. The recovery is fairly fast, and happens to exhibit an indigenous fast-soft recovery characteristic making it near ideal for many switching applications. But, in general it is the low forward drop that generally marks this device for a specific circuit application. Schottky diodes have a couple of undesirable attributes. They exhibit a higher leakage current than their silicon junction brethren, as well as limited blocking voltge due to their junction structure. These two characteristics often negate it from being used in many applications.