D1 and R1 are reference designators. An assembly number is a part number assigned to an assembled and test unit. This would be the number used if someone wanted to order a replacement device.
In a manufacturing company, everything has to have a part number. This makes it possible to order things from other companies, and keep track of the parts needed to build something. If you have ten different pc board assemblies in your product or across multiple products in a company, just calling them "the LED board" or "the motor board" is not good enough. If you assign a unique part number to the pc board (simple PCB, bare PCB, empty board, etc.), it is easier to discuss with the board maker, re-order it in the future, and track changes to the design. Typically the board has a part number and a revision level, such as pcb part number 123-456 Rev. A.
Separate from that is the Assembly Number. This is the part number for the completed assembly, the pc board and all of its components, soldered on, test, calibrated or adjusted, and ready to go into something. Again, it is common for an assembly to have a number with a revision field to track changes to the design in the future.
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