Curb is a thickening of the plantar ligament detectable as a fibrous swelling on the plantar surface of the fibular tarsal bone.

It results from a strain of the ligament itself usually over extension caused by a stumble or slip. It is seen as a visible swelling seen from a lateral view on the back of the hock travelling distally from the point of hock. Lameness may also be present particularly when first forming. May be considered a blemish in the show ring however this is only cosmetic. Weak hind limb conformation is usually the underlying factor as to why horses get this.
False curb is an apparent swelling of the plantar ligament which is actually just a prominent fourth tarsal bone or an anterior deviation of the fibular tarsal bone. Neither is very serious.
Veterinary advice may well be a case of anti-inflammatory drugs but usually rest is the given treatment and should clear up in 6 weeks. This leaves little to do as a farrier, shoeing with width and length to support the hocks is the best thing to do.