What is an "Exemplified Copy" and what is the court's fee to provide such a copy?

An Exemplified Copy is:

An authenticated copy; a copy of a public document or record verified by the seal of the court.

Source: BALLENTINE'S LAW DICTIONARY, Copyright (c) 1969 Lexis Law Publishing, a division of Reed Elsevier, plc.

An exemplified copy's authenticity is sworn to by the clerk of the court and the clerk's signature is further sworn to by the judge.  The court's seal is stamped through all copies, including the sworn authenticity statements of the clerk and judge.

An exemplified copy may be required when the copy is to be filed with a court in another state or country.

The fee charged by courts in Washington State for an exemplified copy is set by statute.  See RCW 36.18.016(4) - Various fees collected - Not subject to division for superior court clerk's fees and RCW 3.62.060 - Filing fees in civil cases—Surcharge—Fees allowed as court costs for courts of limited jurisdiction fees.  You will note in both laws that it costs more for an exemplified copy than for a certified copy.