difference in reverse voltage of diodes?
Schottky diodes tend to have lower forward voltage at the same current than similar conventional diodes, but also tend to have considerably higher reverse leakage. One follows from the other if you look at the Shockley diode equation. 

At high junction temperature you can have VERY significant reverse current flowing in a large low-voltage Schottky diode (tens or even hundreds of mA). 

Usually a 1N400x or even a 1N4148 (200mA rated diode) is fine for the flyback diode on a small relay coil. It only sees the coil current and only briefly.