There are two lines of development in the history of capabilities: hardware and software. The ideas precede the name especially in the hardware line of development. Henry Levy’s book Capability-Based Computer Systems is a good history of the hardware developments.
Capability like descriptors were perhaps the earliest schemes to control the access of problem programs to real memory, but soon the development of virtual memory supplanted the descriptor schemes. Most modern computers have two modes of operation; the privileged and problem modes. The virtual memory provides to the problem program something much like the real memory in that the problem program uses ordinary numbers as addresses to access its memory but those addresses are first translated by some memory mapping hardware to real addresses before real memory is accessed. The privileged program controls this map and thus limits what real memory the problem programs can access. These memory maps were conceived as schemes for the privileged program to provide to the problem program the same simple memory model that program tools, such as compilers, had adapted to. Descriptors required that user code reference those descriptors. While the flat memory model was easier to explain and implement, it was arguably harder for the compiler which had to compile instructions to compute addresses of arrays laid out in flat memory.
Some capability work proceeded with hardware using such memory maps. Cal TSS was designed for a Control Data 6400. The Hydra system, described in Levy’s book, used largely standard hardware. Keykos and Eros use standard hardware.