Orange bricks? Those are usually for looks, or to cover an outside wall. They’re too thin to be structural. Well I’d hope so anyways.

Clay bricks can definitely be structural, and often are in older buildings. The key is that when they are structural, the wall will almost^1^ always be made out of two or three wythes instead of just one. If you're trying to figure out if the wall has multiple wythes but you don't have access to look at the sides/top/thickness of it, you can also tell by the fact that there would be occasional half-width bricks every few courses (because those bricks are turned 90° in order to span two wythes and tie the wall together). If the entire height of the wall is running-bond with no interruptions, then it's very likely^1^ ^again^ a brick veneer and not structural.

^1^ Apparently there are exceptions where a structural wall can be made out of only one layer. I'm not sure I'd trust a building built that way, though...