In WA, there is no state trial court. In WA, the highest trial court in each county is the superior court.
Each county may also have district courts. (Small claims is a department of the district court.)
The difference between superior court and district court is generally the dollar amount. Some types of cases must be pursued in superior court.
RCW 3.66.020 (Civil jurisdiction) specifies what must be filed in district court.
Each city may have its municipal court.
On the federal level, the trial court is the district court.
If there are federal issues, the case likely would be in federal court.
If the case is solely about state laws, it would not be filed in federal court.
You should review the specific facts with your attorney to find out your legal options.