How to know if a diode is Schottky or power Schottky?
The distinction between a "Schottky Diode" and a "Power Schottky Diode" is notional, essentially marketing terminology.

You would choose your diode depending on the maximum current expected to flow through it in forward bias operation. So just buy whatever can handle your worst-case current and is rated for the desired junction voltage.

Typically, manufacturers indicate high current (1 Amperes and up) Shottky diodes as power Schottky, though IIRC even some 100 mA rated ones have a "Power Schottky" mentioned in the datasheet.