"A DSP" implies an actual real object like a chip. "DSP" is a term used to describe "Digital Signal Processing". There is a difference between the two meanings. Any chip that has processing power may be considered for "Digital Signal Processing" capabilities. Hence, an 8051 may be used to find a maximum on a temperature that is polled every 2 hours and this would be considered a crude form of "DSP". You are correct in what you say, but the way you worded your phrases makes the 8051 sound like it cannot perform analytical expressions.

I do disagree with


The whole essence is that the pipelined architecture means that the uprocessor will be further behind than the ucontroller. There are other time wasting benefits of the uprocessor that disallows for proper timing controls, such as, the access to memory. You make the claim that uprocessors can handle interrupts just as quickly, but the interrupt latency is not well defined like a ucontroller. On a ucontroller one has a guranteed latency and on a uprocessor one does not.

Still yet, if one needs control use a controller, if one needs to control multiple controllers based on their feedback use a processor capable of processing the feedback from the controllers.