No, they can't be used interchangeably most of the time. He's on a business trip suggests that he is out of town. The word trip makes it feel like a long distance. He's away on business can be used for a short distance but it can also but used for a long distance.

No, you can't use them interchangeably in all cases. Firstly, you have missed out an article. He's on _a_ business trip. Secondly, "He's away on business" is more general. It could possibly mean that he is just away from the office, so might still be somewhere local, in which case "on a trip" is not quite correct. But in most cases, yes, they are the same idea.