Suppose you have a small-signal audio output implemented as an op-amp stage. If the op-amp has no short-circuit or thermal protection, and you ask it to drive a short circuit, it will probably be permanently damaged. This is true even if the output is AC coupled via a capacitor because the capacitor is transparent to the AC signal, which could have a large signal swing, resulting in a large AC current. An AC short is just as bad as a DC short.
Analog inputs can usually be shorted. This is because they frequently are. Output circuits usually have a low impedance, often very low: close to zero. Furthermore, outputs sometimes go to 0V, like when there is no signal. A low impedance at 0V is a virtual ground: the input is basically grounded when driven at 0V by a low-impedance output. It's even a good idea for unused inputs to be grounded, to reduce opportunities for noise to enter into the device. Sometimes switched input jacks are used to automatically ground inputs when the plug is removed.