There sure is a lot of confusion out there about individual & family coverage in California (and elsewhere).
Quite simply, it's all Obama Care. There are two channels to purchase coverage but all of it complies with the ACA by law. They are not separate markets, just separate channels within a market with some variations in terms of carriers and subsidies.
One, you can purchase your coverage from the exchange (Covered CA) if you want to get some money from Obama to subsidize your premiums/benefits and you are eligible for help.
Two, you can pay the full boat yourself and purchase outside of Covered CA in the private market. Those plans must still comply with the ACA standards and must at least offer 'mirrors' of the exchange (Covered CA) plans (there can be extras in the private channel but they still have to meet metal and ACA standards).
It all comes down to only where the premium $$ are coming from. Otherwise, all plans are part of a single market risk pool and all plans must comply with ACA requirements.
On March 31 Open Enrollment closes for the year and you cannot purchase a policy unless you have a qualifying event outside of open enrollment, on exchange or off exchange.
The exchange is where you get some of Obama's money, the private market is where you spend you own money. Otherwise, they are no different. Networks are identical as well for those carriers selling on-exchange (who also must sell the same plans in the private market).
A true private non-ObamaCare market does not exist in California for individual & family coverage.