1. When hitting your draw can complete a higher one card straight. For example if you have something like 78 and the board is 9TQ. It looks like you have an open-end straight, but hitting a J is not great because any one-card K is a higher straight. Your draw really sucks in this case.
2. When hitting your draw makes a one card lower straight. For example if you have AT and the board is 9JQ. If you're up against another T and you hit a K, he will also have a straight, but you'll have the nuts and likely get paid off. In this case your draw is better than a normal straight draw because your implied odds are very good.