The 6507 is a "cut down" version of their popular 6502. In order to reduce costs the 6507 included fewer address pins, 13 of them instead of the 6502's 16. This allowed the CPU to address only 8kB of memory, which at the time was considered to be a lot. It can also not service external interrupts. The 6507 is otherwise identical to the 6502.
The 6507 was only widely used in two applications, the Atari 2600 and the Atari 8-bit floppy disk controller for the 810 and 1050 drives. In the 2600, the system was further limited by the design of the cartridge slot, which allowed for only 4kB to be addressed.
Most other machines, notably the home computers used the "full" 6502 in order to allow for more memory. By the time the 6502 line was becoming widely used around 1980, memory prices had fallen to the point where the 6507 was no longer a worthwhile simplification.