A DSP is basically a highly specialized microprocessor designed to process certain mathematically intensive operations very quickly - usually with the goal of real time operation with respect to input and output.
Whereas a typical CPU is reasonably flexible, DSPs can only perform a limited set of operations, but they generally can perform these operations at a higher speed than CPUs. At the very least, dedicated DSPs in a computer free the CPU to do other operations. Often the CPU could perform these operations, but it is either not practical or simply advantageous to do them on a DSP.
In an audio processing application, I'm not aware of any DSP effects that could not be duplicated on any modern CPU. However, because the DSP might be able to do in N^2 time what the CPU does in N^4 (or worse) with respect to input size N, CPUs would not be able to run as many plugins as a DSP, or in extreme cases, might not be able to run a plugin in real time.
I not aware of the performance requirements of the TC Works plugins, but rest assured that if the same code was compiled to run on a CPU, they would sound the same.
Digital is absolute.