The difference between CASSCF and MCSCF methods
Both methods optimize orbitals and CI coefficients. MCSCF is the more general term, while CASSCF is a special type of MCSCF. 

As the name Multi-Configurational Self Consistent Field already implies, it combines the Configuration Interaction method with the SCF method (Hartree-Fock). Since this combination increases complexity of the wave function, one usually applies restrictions to both sets of parameters (CI and orbital coefficients). For example core orbitals may be kept fixed (frozen) or only a small subset of configurations is considered.

Regarding the selection of configurations, there are various possible approaches. For example:


hand selecting configurations using chemical intuition or some other a priori knowledge
selecting a subset of orbitals, which should at least cover the HOMO and LUMO. In this active space one considers all possible configurations, hence Complete Active Space Self Consistent Field (CASSCF)
restricting configurations only to certain excitation levels (e.g. Singles and Doubles) within the active space: Restricted Avtive Space Self Consistent Field (RASSCF)


So CASSCF is a special variant of MCSCF, therefore there is not really a difference between the two. Although not every MCSCF is necessarily  a CASSCF, the later is the most common type.