These coprocessors are external chips, designed before floating point math became standard on CPUs.
For example, when an instruction requires any address calculations, the main CPU handles them before the 68881 takes control.
Motorola claimed in some marketing literature that it executes some instructions 40% faster than a 68881 at the same clock speed, though this did not reflect typical performance, as seen by its more modest improvement in the table below.
The most important software incompatibility is that the 68882 uses a larger FSAVE state frame, which affects UNIX and other preemptive multitasking OSes that had to be modified to allocate more space for it.
The 68881 or 68882 were used in the Sun Microsystems Sun-3 workstations, IBM RT PC workstations, Apple Computer Macintosh II family, NeXT Computer, Sharp X68000, Amiga 3000, Convergent Technologies MightyFrame, Atari Mega STE, TT, and Falcon.