Other than has one common usage to indicate exceptions:
There's nothing to eat, other than ramen.
And a less common but generally recognised usage that seems closer to different:
Don't try to be other than you are.
Really, at root they are the same meaning. However, they way they are used feels different. Generally speaking, the two verbs in the second usage - be and seem in your examples, or two lots of be in mine - should be linking verbs, and it just suggests the possibility of being, seeming, looking (etc) different things.
It is perfectly idiomatic, though it has a sense of feeling like an older, more formal, or more artsy usage.