There was originally supposed to be an F-18 Hornet fighter aircraft and a separate A-18 Hornet dedicated ground attack aircraft; the term "F/A-18 Hornet" was originally coined as an informal version to refer to both versions together. When the F-18 and A-18 were ultimately merged into a single multirole aircraft design, the manufacturer sought to highlight this versatility by seeking "F/A-18 Hornet" as the official designation, even though such a designation violates the tri-service designation rules and is completely unnecessary; the rules already explicitly state that multirole fighters are included under the designation "F".
Note that for a while, the F-22 Raptor was informally referred to as the F/A-22; it is not clear whether this refers to an A-18 style separate ground attack variant, or potential revision of the design from a pure "air dominance" fighter to a multirole aircraft. In any case, the Raptor ultimately remained a pure air-to-air bird with only the most rudimentary ground attack capacity, and was officially designated as "F-22".