Correct for the current iteration of the lore which had many retcons, but I was mainly talking about the preWoW lore.
All orcs were green (except for the chaos orcs in WC3 of course), and that's also why the trolls and the goblins were green : they were in the Horde so green "fitted" their faction.
When the lore was detailed many years after, they tried to explain everything. This made the lore much more complete, but at the root of everything, there are these simplistic design decisions every studios used to make in the 90's.