Every STD policy has different features. Your Human Resources department (or your insurance agent if you have an individual policy) is usually the best source of information about your specific plan.
Short-Term Disability (STD) Insurance is not a government benefit, and it is not connected to any public benefit program. It is private insurance coverage that you get through a private company. To find out if you have STD coverage through your employer, talk to your Human Resources person.
There is a totally separate public benefit program that also helps people who become disabled for up to a year. It is called State Disability Insurance (SDI). It covers most people in California who are working. If you become disabled and are unable to do your job, you may be able to get SDI benefits, whether or not you also get STD. To learn more about SDI, read DB101's SDI article.
Note: If you are looking for information about Social Security benefits for people with disabilities, see DB101's Social Security Disability Insurance (SSDI) article and DB101's Supplemental Security Income (SSI) article.