With that processor board, you have a system processor (also sometimes called host processor) connected to an auxiliary processor that the system processor gives work to and controls. If it were closely coupled to the host processor, over a system or special-purpose bus and sharing the instruction set architecture, it would be a co-processor. A loosely coupled processor attached by a peripheral bus with its own instruction set architecture is more commonly an auxiliary processor.
Terminology changes if the subordinate and computation-only status of your device changes.
If it were not a general purpose development board but a specialized product, and its task were related to storage or communications rather than simply high-speed computational tasks, you would have an intelligent peripheral or smart peripheral with an auxiliary processor on board. If your processor were the determiner of the work to be done, and the attached Linux machine were there purely for the communications with the outside world, then the Linux machine would be a front-end processor or I/O processor and your processor would itself be the main or host processor.
- Martin H. Weik (2000). Computer Science and Communications Dictionary. Springer. ISBN 9780792384250.