Two air carrier aircraft with similar call signs confused both the flight crews and ATC when clearances intended for one were accepted and read back by the other.

Narrative

The SAN JOSE 9 Departure was initially uneventful and we leveled off at FL 190 awaiting hand-off to the higher sector. After being level at FL 190 for a little while; we were handed off to Oakland and received a clearance to climb and maintain FL 230 and to expedite up to FL 230. We acknowledged with a complete read back including the full call sign; altitudes; and the expedite request. As we were passing FL 200; another clearance was given to another aircraft to climb to FL 230 and this aircraft had a call sign that was very similar to ours. It was at this point that the Pilots of both aircraft and the Controller realized that we had confusion on which aircraft received the correct clearance. After a quick query on aircraft positions from the Controller; both aircraft were correctly identified and we were told we had gotten the wrong clearance and were on the wrong OAK frequency. We descended from FL 20.5 back to FL 190. After being given a new Oakland frequency; we continued the remainder of the flight uneventfully. At no time were there any traffic conflicts.Once both aircraft showed up on frequency; the confusion was obvious. There was lot of heavy rain and weather in the sector all morning and SJC just had switched from south flow to north flow so this may have also disrupted a normal flow.