Technically a short circuit just means a connection across any two points where the resistance is low enough to "too much" current to flow. "Too much" depends on the circuit itself. For a computer circuit 10mA may be too much. For a small motor, 50A might be too much. For a power grid it might be hundreds of amps. It's more of a qualitative term than a quantitative term.
For example, if you got a large 12V Lithium Polymer battery and connected a 12 ohm resistance across it so there was 1A of current flow and the battery could provide that current without overheating and the resistor is large enough to dissipate the heat, it's not a short circuit.
But if the battery was too small to provide that current without overheating or the resistor was too small so that it got too hot, it might be considered a short-circuit.
THe closest definition I can come up with for a short-circuit resistance is a resistance that is "for all intents and purposes" is zero, negligible, or very small for the circuit in question.