These are two unrelated concepts. Certainly not all entangled states are bound states.
A configuration of objects is called a bound state when it has less energy than the configuration in which the objects are kept far away from each other (or from any external potentials that you apply). You can use this definition in both classical and quantum-mechanical systems.
An entangled state is a purely quantum-mechanical concept which has nothing to do with energy. Separated particles are said to be entangled when measurements performed on different particles are correlated. Namely, if measuring a property of particle 1 teaches us something about a separated particle 2, then the particles are in an entangled state.