Hi, I have found "hat" many times and "helmet" a lot less, but it looks like "helmet" should be the correct term for that.

So I'm asking if I should keep with "american football hat" because of the use or should I say "helmet".

 

It's always "helmet," if you're referring to the headgear that players wear during a game.

 

There are brimmed and knit hats with football logos embroidered as well as helmets used while playing.

Here is a picture of a brimmed NY Giants foot ball hat: http://www.beertripper.com/OffTopic/2012/Sarah_Bolger/Sarah_Bolger_New_York_Giants_cap.jpg

Here is a knit hat: http://www.zappos.com/images/z/2/5/7/2/7/3/2572733-p-4x.jpg

Here is a photo showing two guys wearing helmets: http://prod.static.giants.clubs.nfl.com/assets/images/imported/NYG/giants_uniforms/jersey6.jpg

 

Ohhh I see, I understand perfecly. it's helmet then. Thank you.