Actually, the zIIP and zAAP processors for "accelerating" java or db2 workloads are identical to the other processors in terms of hardware; the underlying firmware just loads different microcode onto the chip to prevent it running a full Z/OS instance.
The difference is one of licensing -- IBM charges less for activating a core if you can only run java|db2|linux on it.
They may actually put an accelerator in the system at some point in the future, but for now it's just a way of using more processors without spending as much.
The specialty procs also tend to run at full speed where IBM usually caps the general processors. My workplace recently upgraded from two Z9's to two Z196's and the difference is astounding.
The first mainframe I used, more than 25 years ago, had about a hundred 3278's connected to it. And it was still fast for interactive use when compared to the 8-bit computers of its day. This Z9 was probably commissioned after 2005.