What is the difference between an open and a short?

An open (circuit) is where insufficient (often zero) current flow where some is expected. In this case, little or no work is done.

A short (circuit) is where high (often infinite or as limited by the power supply) current flows where only some is expected. In this case also, little or no work is done by the device intended, but there is enough current to trip (or blow) the protective device (fuse or circuit breaker).