Two basic types of longbows:
When they are unstrung there are ones that are straight and one that have some curves somewhere in them.
Reflex is the curve of the limbs towards the tips or ends of the bow. If you hold a bow up like you were about to shoot it, but it was unstrung, the tips would curve away from you. The actual relex isn't the tips, however, it is the limbs sweeping back towards you.
Deflex is the curve in the riser (handle) area. Unlike the reflex, deflex moves the handle towards the target...
In a nutshell, reflex is towards you, deflex is away.
Straight longbows, sometimes synonymous with a Howard Hill style bow, have no or very little sweep or bend in the limbs when the bow is unstrung.
A static recurve the tips do not uncoil upon drawing the bow back. The stiff tips make the middle portion of the limbs work harder. Static recurves have been around for centuries.
Essentially there are only static and non static recurves, but there are design differences such as a deflexed riser, etc.
Hope this helps,
Clear as mud?
Mike