I'll toss in my two bits.
Shroud means cloth, or to clothe.
Shrouds on a ship would seem to refer to the effect of a mass or collection of ropes clothing an otherwise naked spar.
I'd say if it's a single rope or wire, such as a stack stay, it's a stay. If it's one of a collection of same, and reasonably coplanar, then those could be called shrouds.