'Short Circuit' gets used in two different ways.
In the context of a battery (or any power source), we usually mean it to be a load that is far too large for the source. Any battery, whether a high voltage or low voltage battery, will be 'short-circuited' by putting a low or zero resistance load on it.
A short circuit usually produces damaging conditions for the battery, and the load, if maintained for enough time. At best, the battery will be run down quickly. At worst, the battery may catch fire, burst itself or its container, or the load start a fire.
The wiring to a high current battery, like a car battery for instance, will invariably be protected by a fuse, which opens in the event of a short circuit. The wiring to a low current battery may not need protection, if the short-circuit current is low enough for any practical wire. Given this, there may be some sense, hinted at in your question, that for high current batteries, a short circuit is an issue, where it is not for low current batteries. For instance a PP3 or CR2032 battery, while it will be run down by a short circuit, is most unlikely to start a fire as a result.
In circuit analysis, a short circuit is an ideal zero resistance, that will support any current with zero voltage across it.