Snapback, trucker, and dad hat.
For a snapback, define the crown profile, panel arrangement, brim shape, and closure. Structured and unstructured directions create different appearances even before decoration is added. A trucker brief should address the front construction and mesh-back relationship, including the visual balance between the panels and the adjustment at the rear.
Dad hats are often used to communicate a more relaxed direction, but the name alone does not specify crown depth, brim curve, or fabric. Supply side and front references, not only a straight-on logo image. The sample should be reviewed on an appropriate head reference so the silhouette is evaluated as worn, not just standing on a table.