Dinneen’s dictionary describes coill as
a wood; a grove
and foraighis (a pre-reform spelling of foraois) as
a forest; a wild beast’s lair (also a gluttonous person or beast)
My knowledge of the distinction between coillte and foraois is limited to what I can glean from dictionaries; Dinneen’s entries suggest that the distinction between coillte and foraois is similar to the distinction between “woods” and “forest”.
The Irish body in charge of forestry is called Coillte..
The way I understand it, from various sources:
Coill is used when the focus is on trees, and their wood... Thus woods.
Foraois is focus on bigger forest, but also on forest/woods from the point if view of the folliage coverage, a place to live, hunt or hide. Rather than just a grouping of trees.