Hepatitis <B>B</B> <B>s</B>erum <B>A</B>nti<B>b</B>ody
No - it's hepatitis B SURFACE antibody. There are 3 types of hepatitis B antibody that are commonly measured: s (surface), e and c (core).
Positive sAb means previous *successful* vaccination, or previous exposure to the virus with development of immunity.
If you have had a course of vaccinations, and have a negative HBsAb test, then the vaccination has failed and you are not immune. Many jobs in e.g. healthcare require a positive HBsAb test as proof of immunity.
Positive eAb or cAb mean previous infection.