I don't know that the cloak styles are anything more than different engraving styles, but in keeping with RIC VII tradition here is an unlisted coin. RIC only lists this type as Sol with chlamys over left shoulder. Lech has another example here-
http://www.forumancientcoins.com/notinric/7lon-147_cri.htmlCrispus
A.D. 318
18x20mm 3.3 gm
FL IVL CRISPVS NOB CAES; laureate and cuirassed bust.
SOLI INVICTO COMITI; Sol rad., stg. r., raising r. hand, Victory on globe in l., chlamys spread,
Crescent in left field.
In ex. PLN
Cf. RIC VII London 143