Understanding U.S. visas can be very complex and difficult. Depending on the purpose of your visit in the U.S., you will be classified under either 1) immigrant visa category or 2) nonimmigrant visa category.
Besides H-1B and J-1, some other common non-immigrant visa categories sponsored by UCSF are:
E3: Work visa for citizens of Australia
O-1 & O-3: Extraordinary ability in Sciences, Arts, Education, Business, or Athletics
TN: Trade visa for citizens of Canada and Mexico
Immigrant visas are for those who intend to stay in the U.S. permanently. See "Permanent Resident" for additional information.