Hi Brianna
Magnet schools are part of the regular public school system, and follow the same administrative rules as the other schools in the same district. Typically, a magnet school is designed to have a particular emphasis, for example some magnet schools concentrate on having a very strong arts program, others maybe on a high level science program, and they can provide parents more of an option in public education. "Fundamental" magnet schools, which emphasized rigorous 'traditional' reading, writing, 'rithmetic methods, became very popular at the elementary school level a decade or ago when test scores were plummeting. (Before NCLB.)
I think anybody living in a school district can apply for Magnet School, but the school doesn't have to consider everyone equally. They can consider academic performance or other student assessments in deciding which students to accept. Requiring parent and/or students to sign contracts which outline student and parent obligations are very common.
Charter schools are much looser administratively. They do not "have" to follow the same rules as the other schools. They don't even have to be geographically located within the district. They have a great deal more freedom hiring and firing teachers or administrators. They tend to be more experimental. I know some charter schools which are essentially district-assisted homeschools. A Charter is something like a contract, usually having an expiration date after a period of 5ish years or so, at which time the district can renew the charter as-is or with new conditions, or they can let the Charter die without renewing it.
Charter's are more controversial because they are so loosely monitored. But my children's middle school (which was the only available MS except continuation school and considered superior compared with like schools in other districts in the area) went Charter about 15 years ago because it loosened the school from administrative hamstrings.
I live in California too. The education codes covering the state fill volumes and volumes, just full of bureaucratic stupidity which interferes sometimes with the best decision making at a particular school. The Charters don't have complete freedom from it, but much more so than Magnet schools. Whether Charters end up making the most responsible use of that freedom can vary a great deal from school to school.