To answer this question it is easiest to firstly define both a weak and strong acid.

A strong acid is an acid that completely dissociates into its component ions in solution.

A weak acid only undergoes partial dissociation in solution, this leads to an equilibrium between the solvated undissociated acid and its component ions.

Therefore the difference between the two is that the strong acid completely dissociates, whereas the weak acid only partially dissociates.