The primary change from the 6502 was the addition of an 8-bit general purpose I/O port (only six I/O pins were available in the most common version of the 6510). In addition, the address bus could be made tristate.
The 6510 was only widely used in the Commodore 64 home computer (and in significantly smaller numbers in the C64's portable version, the SX-64). In both the C64 and SX-64 the extra pins of the processor were used to control the computer's memory map, and in the C64 also for controlling the electric motor of the Datassette tape recorder. It was possible, by writing the correct bit pattern to the processor at address $01, to completely expose the full 64KB of RAM in the C64, leaving no ROM or I/O hardware exposed.
The 7501/8501 variant of the 6510 was used in Commodore's C16, C116 and Plus/4 home computers, and the 2 MHz-capable 8502 variant was used in the Commodore C128. All these CPUs are opcode compatible (including undocumented opcodes), except the 8502, where some differences concerning the undocumented opcodes have been reported.