Here's the facts:
- An orc is a big green dude. Usually.
- Some settings appropriate them as evil creatures that are righteous targets. Fine, that's their thing.
- Orcish culture is any culture which belongs to Orcs. (In some settings, this is violent and barbaric. In some settings, it is not.)
- Any culture the Orcs have is Orcish. (Them having it makes it Orcish.)
- I can write a setting which features big green Orcs which have a peaceful shamanic existence with very little fighting and respect and dignity for other lives. There are no other kinds of Orcs, and never have been.