A precautionary landing is done in cases where it would be inadvisable to continue to your destination e.g. bad weather, night, low fuel, and is therefore a precaution in case you crash and die.
Short field landing = a landing utilising the maximum landing performance of the aircraft i.e max flaps, braking, reverse if applicable.
No idea about the Tiger Moth stuff but I would guess a no leading edge devices landing (didn't know thay had flaps).