Not all acids are the same. What's at play isn't only the amount of free protons but also what else is disassociating. For instance, hydrofluoric acid is considered a weak acid but it can severely burn (pretty slowly but it will get you) or even kill you. The fluoride group will consume the calcium ions in your blood and possibly send you into cardiac arrest.

Any compound with a hydrogen ion that can dissociate in solution is technically called an acid, but that doesn't mean it's acidic properties are the most relevant.