What Differentiates the chemical behavior of a strong acid from a weak acid?

I can say from my personal high school experience that a weak acid like HCl does not spill out strongly when drops of water are added to it but when drops of a strong acid like Acetic or Concentrated Sulphuric Acid(H2SO4) are added to water then their liquid can splash out on our face or body. Hence, we have to be careful and always keep in mind that acid should be added to water and not the reverse while performing such chemical experiments. I think that chemical consultants can give you a better explanation than me as they are experts in this field.