Damsel

This little damsel fly fluttered by looking like a butterfly.  She landed long enough for a portrait.

 

Jewelwing

They fly like butterflies and perch like dragonflies.  They fold their wings which shows them to be Damselflies.

These are Ebony Jewelwings (see here)

 

Little what?

It looks like a dragonfly, but it flew like a butterfly, and folded its wings like one too.  
Well, it's neither.  It is an Ebony Damselfly!  (see here)