Plain 4: The "Plain 4" designation indicates the numeral "4" in the date on the coin. The "Plain 4" variety lacks any additional decorative elements or serif-like features on the numeral, making it a simpler and plainer representation.
Restrike: The term "Restrike" implies that the coin was struck at a later date than the original year of issue. In the context of early American coinage, restrikes were often produced using original dies but with the intention of creating additional examples for collectors or commemorative purposes.
The 1804 Turban Head Gold $10 Eagle is a part of the early history of U.S. coinage, featuring the design work of John Reich.
Given the age and historical significance of coins from this era, the availability of such coins in proof format and restrikes adds further intrigue to their numismatic appeal.
If you possess a coin fitting this description, it is advisable to have it authenticated and graded by reputable numismatic experts or professional grading services.