San Francisco has a few ordinances that go beyond what state law criminalizes or requires. You can pull up its Municipal Code online and search for the term "firearm" to see all its ordinances. The main ones that I know of are a requirement that all handguns be locked away in the home when not on one's person; a a ban on the discharge of firearms, and a ban on the sale of ammunition that doesn't have "sporting purpose" (whatever that is). You are correct that all of these ordinances are being challenged in court, my firm (Michel & Associates, PC) is counsel for plaintiffs (who include multiple individuals and the NRA) in that suit, Jackson v. San Francicso. I am not the main attorney on that case, but I have worked on it. If you would like to read more about the Jackson lawsuit there is information available at www.calgunlaws.com, just search the term "Jackson".
In addition to the ordinances I mentioned, I know there are also ordinances on firearm dealers in San Fran. For example, they cannot sell handguns of a certain size, they have to take an inventory of all firearm sales beyond what is required by state and federal law, and they are required to register some ammunition sales. Some of these ordinances will likely face challenge in the future.
One more, in California, the only way you may lawfully carry a firearm for self-defense (barring extreme circumstances) is if you have a license to do so issued from the sheriff of the county (or chief of police of you city). It is almost impossible to obtain such a license in San Francisco. You have to be Dianne Feinstein, a four-star general, or someone else whose life is worth more than yours (I am being sarcastic if you don't get it).
All my comments here are intended for general legal purposes. None of my comments here establish an attorney-client relationship with anyone. None of my comments should be relied on in taking legal action without first consulting an attorney.
Same gun laws as in the rest of the State of California. There's a big long list of them. Try asking a specific question.
Mr. Feasel is a former Deputy DA in the SF Bay Area with over 10 years of criminal law experience. Nothing stated on this site shall in anyway be construed as legal advice, or as creating any attorney/client relationship. If you would like to hire Mr. Feasel to further investigate your situation, feel free to contact him thru this site.
It's not a question of SF's gun laws. CA's gun laws are state wide, however, each community can put restrictions on legal gun sales that go beyond state law. In many counties in CA it is possible to get a concealed firearm permit. It is theoretically possible to do so in SF but the requirements are so stringently enforced that almost nobody can get such a permit here. That's local politics, not gun laws.