It all has to do with time zones -- specifically the old Greenwich Mean Time. Many calendars will list the moon phases (and dates the seasons change) as when it occurs at Greenwich Mean Time, which is 7 hours ahead of Pacific Daylight Time, and 8 hours ahead of Pacific Standard Time.
This month, the full moon was at 4:48 a.m. GMT on Aug. 12. But that's actually 9:48 p.m. on Aug. 11 in Seattle. So our full moon is Aug. 11, but it'll be listed as Aug. 12 in many sources.
You can find the exact times at this Web site -- aa.usno.navy.mil. Just be sure to adjust for GMT time.