The newest method of homeschooling is to use independent study, distance learning, and homeschooling programs developed by various charter schools throughout the state.
Charter schools are state funded. They may be operated by nonprofit organizations, private businesses or individuals, or even public school districts or county education departments. They operate under a charter granted to them by a public school district, a county board of education, or the state.
There are different kinds of charter schools and a subset of them offer independent study programs in which children are primarily taught at home. These can also vary a lot. Some require use of an online school program. Some require attendance at a certain number of in-person classes. Some do not have any required attendance other than some kind of regular meeting, usually monthly, with a credentialed teacher. Some offer learning resources for parents to choose from within a budget. Some charter schools offer students the opportunity to compete on public school sports teams, while others are only distance learning programs using the Internet. They all require standardized testing and reporting, usually with work samples to a credentialed teacher.
They are publicly funded so, in that sense, students are public school students who are being primarily educated at home by their parents.
In some other states there is a legal definition for homeschooling and enrollment in a charter school program is legally not homeschooling. In California, however, we do not have a legal definition of the term homeschooling and so using a charter program is just one of the various ways to homeschool here.
Charter schools are limited to serving students in their home county or contiguous counties. As with all programs, you will need to thoroughly investigate the program in order to determine if it will meet your needs.
Further information on charter schools can be found at http://www.cde.ca.gov/ds/si/cs/ or http://www.chartervoice.org