Yeah, that's pretty much what they are. The strong willed are enhanced by Jenova cells and Mako, but the weak willed (like Cloud) go off their heads. Sephiroth (at the Great Crater for most of the game) manipulates the clones and Jenova to do his work. The process used on members of Soldier and to create "the clones" is essentially the same. But Hojo for some reason calls them "Copies"... I am not sure if this is deliberate and has some sort of relevance to the plot, or whether the original writers just chose a really lousy word for the process. Maybe there is some mention of this in some official works?
Also, maybe an oversight on the writers' part but at the Temple of the Ancients, Cloud refers to the black cloaked people as Sephiroth's doubles (intended as such like that of Mitosis, and originally laughably translated as "flunkies"), as in, they are linked genetically because of the process they have been through. However, I cannot remember any prior exposition that would tell Cloud that.... Maybe I am just missing something thinking back. The only mention of copies that I can remember prior to this is the report by Hojo which you can choose to read. I will have a good look into this when I go through the game again when this is done.
ps 16 maps left. Should have this done in a week.