I know I'm extremely late to the party, but in you have any doubts about the terminology, in the modern sense, the distinction between armets and close helmets is in the way that they open and close. "Armet" used to be the blanket term for most types of enclosed helmets from that particular period, but it's largely accepted now that close helmets swivel up and forwards and armets swing outwards from the middle to the sides.
Armets tend to also be older designs than close helmets dating to the early 15th century, while close helmets appeared later and derivatives of the close helm were still being used in the early to mid 17th century by some cavalry.