I am currently working under a F1 OPT visa. I noticed that one employer deducted state taxes last year as opposed to the other that deducted local taxes. What is the difference. Do I owe both and what form is used to calculate state/local taxes in CALIFORNIA?
Thanks.

You will have to pay BOTH.

If you work in California, the state has the right to tax your income.

If you work in a specific county or city that has an income tax, that county or city also has the right to tax what you earned in that county or city.

Why would one employer only deduct state taxes and one only deduct local taxes - both are in the same city?

Contact the employer who deducts only local taxes and ask WHY his did not deduct state taxes.

I suspect you will find that the W-2 is in error, and he will need to cut a new one showing the local taxes as being in fact STATE taxes.