There is (or can be) some overlap between the two.
As an example, you may want to create a kernel module that can be configured through the device tree (e.g. binds to an arbitrary SPI/I2C bus, requires hardware-specific config). You can add a node for your module to the device tree and assign it a "compatible" property, which is just an arbitrary string you define to represent your module. If you then make your module export the same string using the MODULE_DEVICE_TABLE macro, the kernel will figure out that your module is the one that implements that node in the device tree, and it will call your module's probe callback to initialize the module, passing in the context from the device tree node (e.g. you can get a reference to the SPI/I2C bus hosting your device).
As I understand it, this is the standard way to implement drivers for devices that sit on buses that don't support automatic detection (e.g. not PCIe / USB).