Abaya is known by many names but the purpose, which is to cover. cut from light Etc, flowing fabric like crepe, Georgette fabric, and chiffon fabric.
Other known abaya styles are front open and the front closed abaya. 
styles Come from Country and region: 
some abaya has embroidery on the black fabric while others are brightly colored and have different forms of artwork across them.

Flared Abaya: This is a modern and new style design of abaya which features beadwork on the edges.
Abaya with bell: It is a long sleeve fit from elbow to shoulder.
Baggy style abaya: A most fashionable looking abaya, Abayas featuring baggy sleeves that give a stylish look and reflect cultural values.
Cuffed sleeves: sleeves which are long and fit strongly like a cuff at the wrist edges. 
Batwing sleeves abaya: resemble the wings of a bat. It  is more likely to be open and have more fall
Abayas with the panel: more people prefer panel work, the abaya is designed in panels, like shirt or lining.
Puffed, long sleeves Balloon shaped sleeves that are tight at the wrist.