For simplicity's sake, let's start with State Marine Reserves, which you did not ask about but will be the backbone of the MLPA networks. No take of any natural resources.
A State Marine Park prohibits commercial fishing. Like reserves, they are not no-motor zones, although the department has the authority to limit access and other non-consumptive activities. They need a good reason to do so. Most typically, they might want to protect a bird nesting area from disturbance. Those are usually conducted under the authority of a special closure, not an MPA.
Back to the park idea, as far as fishing goes, the designation has a lot of flexibility. It could run from all recreational fishing is ok down to almost none.
A State Marine Conservation Area is just as flexible, but does not prohibit commercial fishing unless explicitly stated. They can be nearly as restrictive as reserves, such as in an SMCA that allows hand harvest of kelp only. In MLPA terms, they've been used to allow fishing for species that don't benefit from reserves - pelagics such as salmon and yellowtail. Here in SoCal, we're likely to see them used in water deeper than 30 meters.
SMPs come with jurisdictional red tape that I don't understand fully. They should be placed adjacent to a state park. The park service apparently has the ability to change the regulations if they choose.
Please forgive the long answer. If it wasn't long enough, I'll give it another shot.
