What does exponential look like then?
This is why you sometimes see complexities that are e.g. O(1.3894732894^n) in wikipedia articles on the best known cases for various algorithms.
Typo: O(a^n) is a stronger guarantee than O(b^n) if a < b. It means nothing if a > b.
I actually thought the most likely intended meaning was that an algorithm in O(a^n) must take asymptotically longer than one in O(b^n) as n goes to infinity (if a > b), which isn't true. (For example, when a > b, then every algorithm in O(b^n) is also in O(a^n), but obviously no algorithm can asymptotically require more time than itself.)