Air carrier departure from SEA was questioned by the TRACON controller regarding heading; the reporter indicating the clearance phraseology used by the tower controller was misinterpreted.

Narrative

[We] departed Runway 34R at SEA. Another carrier's MD-80 preceded us by 3-4 miles. We were on the MOUNTAIN SIX Departure. This departure requires a turn to a heading of 070 degrees at 7 DME. I was the non-flying pilot. At approximately 2000' MSL; the Tower asked us if we had the preceding MD-80 in sight. I said we did. Tower the said; 'Maintain visual separation from the MD-80 and start your east turn; contact Departure.' We started a turn to 070 degrees. When we called Departure; upon checking in; Departure asked us our heading. I said turning through 030 degrees. Departure then said turn back left to 340 degrees and asked us if we had the MD-80 in sight. I said we did. Departure then said maintain 6000 feet. Departure then said turn right to 050 degrees and again asked if we had the MD-80 in sight. I said yes. Departure then said cleared direct to XXX (don't remember fix). Departure then gave us a phone number to call. We called them when we landed. The Supervisor said that Tower had NOT cleared us off the SID. He also said that the Tower reviewed the tape and recognized that their transmission could have been misinterpreted by us. What the Tower said was; 'When you start your east turn; maintain visual separation from the MD-80.' We interpreted the transmission as 'START' your east turn. The Supervisor said that the Tower would review terminology that they use to prevent the same thing happening again.