Help distinguishing 13c Italian helmets

[Ernst]

I'm going through the Statutes for the various Bolognese Lombard societies and citizens, and I'm unsure of the distinction among helmets, kettle hats, coifs, etc. Any help or insight is appreciated.
http://archive.org/stream/statutidelles ... 2/mode/1up

The Statutes for the Societa Dei Vari in 1256 require

XXVIIII Statuimus quod quilibet de dicta societate teneatur habere scutum et capelictam de coro vel capellum de ferro et non caçetam, nec debeant eas impignare.

Clearly a shield is required and there's a choice of leather or iron headgear of some type, and a restriction on another. Is this requirement for kettle hats instead of mail coifs or cervellieres?

The Societa Dei Lombardi in 1256 gives its members the choice of "elmum vel caçetum", and while the helm seems clear enough, I'm still only guessing that the caçetum or caçetam is a coif or cervelliere. This statute is also frequently quoted for the likely body armor options of "cubam vel guayferiam vel lamerium".

In 1288, the Societa Dei Vari repeats the same requirements as 1256.

Any insights or ideas?