Obamacare is a nickname for a law. The name of the law is the Affordable Care Act. This law covers medicare, medicaid (called Medi-cal in CA), private insurance and employer based coverage.
Covered CA is California's marketplace. These are private health insurance plans (just like you will buy directly from the insurance company) that have been approved to receive a tax subsidy. They generally have few choices of in-network doctors to make them less costly than plans directly from the insurance.
Since your son is earning more than $4150, he is not your qualifying relative on your taxes. Thus, he is not a tax dependent of yours. But he is likely in the gray area that is "stuck".
- For CoveredCA purposes, he is his own household. Thus he should be eligible for his own subsidy making insurance free or close to free. However, his income is so low, CoveredCA is going to say "hey, you don't get a subsidy you should get free insurance from Medi-Cal". But Medi-Cal says "whoa... we can't do that... he isn't supporting himself. He's not eligible for me".
Most schools in California offer health insurance. In fact, the UCs require you to have health insurance and if you can't prove you have other coverage, they tack on an insurance fee. The community college or university insurance is likely the most cost effective plan (from a pure hard dollars stand point). But it might not provide the best coverage for your son's needs. If that's the case, he will need to purchase private coverage.