[Xiammes]

Aqua Coral was just a reused name for some reason, possibly due to Imai forgetting he'd already used it.

Highly doubtful, this is Imai we are talking about, he wrote a

Hatfield's fragment is officially Rainmaker; he has the ability to actually manipulate the properties of water, making them become like spears or razors or weighty objects,

whereas Nanami just literally controlled waters motion and speed.

Spoiler for picture:

Creates and controls water at will, Hattfield had a lot more control over his water, but they both have the same fragment, just the level expertise varied. Hattfield said that he comes from a family of Rain Dancers in America, he uses that to summon his rain.

the "Aqua Coral" Hatfield uses specifically refers only to his defensive spiral technique

Remember Hattfield is one of Simeon's elite, they never directly reveal ones fragment, and will make you believe its something else. He wouldn't have the power to summon rain and control water at will, because we already know the ability to manipulate water is called Aqua Coral.