In terms of electrical conductivity, acids and bases differ from one another depending on the density of free ions present in them.
A strong acid/base has the ability to conduct electricity readily.
The quantity of ions increases as the strength of the signal increases.
Consider the following scenario: If you connect a bulb in a circuit with a strong acid/base solution, the bulb will glow appropriately;
but, if you connect it with a weak acid/base solution, the bulb will not glow considerably.
It simply relies on the strength of the acid or basic.
Both are capable of conducting electricity.