If you removed the bold texts, you would have been right.
In broad sense, all CPU, co-processor, GPU (accelerator) and DSP are the same, having a calculating (add, subtract etc.) registers that read, calculate and write back from a memory bus. So one can call all of them Processor Unit.
However, in a strict sense within computer industry, they are differentiated on purpose. Accelerator is commonly used as alternative term for GPU for graphical processing acceleration. It is a Processor Unit for sure. But one can not call it CPU because C is Central which is reserved for the Processor Unit that sit on top of the architecture. CPU is the one whole control other PUs such as Co-Processor and GPUs, which the later two never do this task. Another distinction is OS instructions are executed on CPU only. CPU will decide whether to send certain instructions to Co-Processor and GPU or not. CPU can do these work on its own abide slower, but the other two can't do everything CPU can do.
BTW, GPU (accelerator) is a specialized Co-Processor whose early role in the 1990s were offloading mathematical calculation from CPU. Later on GPU showed up to offload the graphical tasks. So GPU is equal in architecture to the Phi chip, not to any CPU.
