what are they, or are they the same?

The Green Man was one of them.

This page tells some about them::

 

http://encyclopaedia-wot.org:8008/creatures/nym.html

 

If my memory serves, they were One Power Constructs created in the age of legends (as encyc-wot says above)

From the BWB:

One particularly interesting fragment records Aes Sedai participating in an avenue of research that led to the development of living constructs made with and/or able to utilize the One Power. Chora trees were one such construct. Their large green trefoil leaves emitted an aura of peace and well-being to any who passed beneath them. The Nym, another construct, were sentient beings with the ability to utilize the One Power for the benefit of plants and growing things. As a nameless scribe in Paaran Disen wrote, "Where a Nym touched, all manner of green and growing things thrived."