The words "concentric" and "DD" (or "double-D") refer to the type of your metal detector's internal coil construction. Most searchcoils (whether round or elliptical) are of concentric construction. A concentric searchcoil has a large transmitter coil, and a smaller receiver coil in the center, usually in the same plane. This coil arrangement is relatively easy to manufacture and its symmetry helps to minimize electrical drift due to time and temperature. It also provides good discrimination on shallow targets.
Some searchcoils (whether round or elliptical) are of DD construction. Double-D's comprise two overlapping D-shaped coils of approximately the same size, one being the transmitter and the other the receiver. The advantages of the DD are greater depth in mineralized soil, a broad sweep pattern, and narrower target response. Its primary disadvantages from a user's point of view are multiple responses on shallow targets and poor discrimination of flat iron objects. Designing and manufacturing them is more difficult because their lack of radial symmetry makes them prone to drift which the design and the manufacturing process must minimize. Manufacturing cost is higher because the coils cannot be wound on high-speed winding equipment.
Double-D's are usually preferred for relic hunting and gold prospecting. Concentrics are usually preferred when searching for modern coins in an area where there is also iron and aluminum trash.
Read more about searchcoils here...