They would be acids.
Most substances that dissociate into constituent ions in aqueous solution are ionic compounds (
However, there some very important covalent compounds that dissociate as well, and they are called acids.
Acids have a few different definitions, but they can be categorized into two main groups: strong acids and weak acids.
Strong acids are those that dissociate essentially completely in solution; i.e. there isn't really an equilibrium established between between the composite ions and the molecule itself. There are seven common strong acids:
(notice there is only one diprotic acid: sulfuric acid)
Weak acids essentially consist of all acids that are not the above seven. They do not dissociate to near completion, and have a measurable equilibrium between molecule and dissociated ions.
Weak acids have an acid dissociation constant, denoted
For example, for the weak acid