If a battery short circuits it just means that somewhere within or outside the battery there is a direct connection between the terminals causing a very low resistance and a high amperage that with burn up the battery.
To recap: the short circuit current is a function of several variables but is mostly determined by the nominal voltage and internal series resistance. If the positive and negative terminals are connected by a wire then the battery is by definition shorted. What the voltage of the battery is does not really matter.
By short circuit we mean an electrical short circuit, a very low resistance path between the positive and negative sides of the cell or cells. A short circuit can be inside a battery cell or external to a battery cell. There are a number of things that can cause an internal short circuit within a battery cell.
A "circuit" is the path electricity follows. A "short" is an electrical connection in a place there shouldn't be one. A short circuit battery would be caused by having the + and - ends of the battery connected together when they should not be.
For large batteries such as those used in Power Stations, short circuit currents may exceed 40k amperes. Even when the battery is not fully charged, the short circuit current is very similar to the published value because the internal resistance does not vary substantially until the cell approaches fully discharged.
Yes, a short circuit can damage a battery. A short circuit happens when there is a low resistance path between the positive and negative terminals of a battery, allowing current to flow freely between them.