Applied mathematics represents a quantitative liberal arts degree. The degree provides the opportunity for combing mathematical thinking with any subject for which mathematics can be productively applied.
In some instances, combining applied mathematics with a particular subject can lead to a program of study that is quite similar to studying that subject itself. For example, applied mathematics with physics as an application area is quite similar to studying physics. On the other hand, there are other instances (combining applied mathematics with music or history) where the degree program would be completely different.
At a professional level the difference between an applied mathematician and a practitioner in a given field can be very small, when the two are working on problems in that field. However, the applied mathematician's primary interest is in the general way that mathematics is applied--and as such also could use [variants of ] the same methods to study other fields.