Strong acids are strong electrolytes, meaning they will be 100% hydrolyzed in water.

In the hydrolysis of HCl:

HCl (g) + H2O (l) --> H3O+ (aq) + Cl- (aq)

there will be no molecules of HCl in solution - they will have all been rendered into ions.

Weak acids are weak electrolytes, meaning less than 100% of the molecules will have hydrolyzed in water.

In the hydrolysis of HF:

HF (g) + H2O (l) --> H3O+ (aq) + F- (aq)

there will be some amount of unreacted HF molecules in solution.

Here is an animation of a strong acid versus a weak acid.

The same concept applies to strong and weak bases.

Here is an animation of strong versus weak bases.