Though the name for the army's cap is 'forage cap' (as it was used for foraging), the navy's did not originate from the army's and is merely called a 'peaked cap.' (Though this is just another case of unification leaving the navy with a strange vocabulary for items that were similar between it and the army.)
If you take the logistics branch's name for them as the correct name, it is a 'man's service dress cap' (the sexual distinction is made despite that women do not wear 'caps' but 'hats'). Hats, by the way, are distinguished by having a brim all around, whereas a cap has none or a partial brim, such as the forage cap or beret.