FLC OF A B737-400 TAXIED FROM THE RAMP BEHIND ANOTHER COMPANY ACFT WITHOUT TAXI CLRNC. GND CTLR ASKED THEM WHERE WERE THEY GOING WHEN CHKING IN. FLC WERE RUSHED TO LEAVE THE GATE FOR ANOTHER COMPANY ACFT THAT NEEDED THEIR GATE.

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THIS WAS AN UNAPPROVED TAXI OCCURRENCE. THE EVENT WAS PRECEDED BY A NONSTANDARD SIT; TFC CONGESTION AND CONGESTED RADIOS; RESULTING IN CONFUSION. HAD TO PUSH BACK FROM GATE AB AT SFO. MARSHALLER'S HEADSET INOP; SO HAD TO RESORT TO HAND SIGNALS. COMPANY ACFT PUSHING BACK SIMULTANEOUSLY FROM GATE AC. ANOTHER COMPANY ACFT HOLDING ON TXWY WAITING TO GET INTO OUR GATE. WHILE COORDINATING WITH MARSHALLER AFTER ENG START; I THOUGHT I HEARD GND CLR US TO TAXI BUT IT WAS THE OTHER COMPANY ACFT WHO PUSHED BACK FROM GATE AC. AFTER 'WAVE OFF' I IMMEDIATELY BEGAN TO TAXI TO CLR 'ALLEYWAY' FROM TXWY TO ALLOW OTHER HOLDING ACFT TO ENTER GATE. APCHING TXWY (NEAR RWY 1L); GND CTLR QUERIED US BY CALL SIGN AND SAID 'DO YOU KNOW WHERE YOU ARE GOING?' FO THEN REALIZED HE FAILED TO CALL GND; TOLD ME AND I STOPPED FOR FURTHER INSTRUCTIONS. I NEED TO PAY CLOSE ATTN TO RADIOS; ESPECIALLY PRIOR TO TAXI AFTER PUSHBACK. (I MISTOOK TAXI CLRNC FOR ANOTHER ACFT AS MY OWN). FORTUNATELY; THERE WERE NO CONFLICTS WITH OTHER ACFT. CTLR TOOK IT WELL; BUT THIS WAS NOT A GOOD THING TO OCCUR ANYWHERE; ESPECIALLY SAN FRANCISCO.