'Applied Mathematics' is a much-used term in modern mathematics, but I've yet to find a universally-agreed upon definition. Given its use as a major category ('pure' vs 'applied') and repository of sundry generalizations ('non-rigorous','relevant', 'not deep', 'critical to science', etc.), surely a precise definition is in order.
In the MSC, there is only one MSC code with this phrase (00A69). Based on this, maybe 'Applied Mathematics' is a field of inquiry which is not important