This is the ancient name for silicon, germanium, galena, and schottky diodes. It comes from the old days when a metal wire was mechanically touched to the galena crystal.
The name is old but the definition is still valid.
A cristal detector is a sqare law, semiconductor, diode working with Vout in the mV range.
The Cristal detector is a basilar component for most advanced measuring instruments.
For a detector diode we want a fast diode (low parasitic capacitance compared to C in parallel LC tank) with a low threshold voltage. This is why Schottky's are used for this purpose. I suppose a while ago crystal diodes would have had agreeing performance, but clearly at higher price.
In average, the price of a second-hand good crystal detector is $100. **broken link removed**
For some applications they are very good, and cannot be replaced by anything, due to a very fast response (~200 pico seconds)
First available crystal diodes as far as I remember were germanium point diodes. They have very low capacitance and knee voltage, even lower than today's shotky diodes. I believe you can stil get AA116 or 1N34 diodes. Price is higher than for nowadays diodes.