Binary format commands are those written in C, C++, FORTRAN, or any other compiler language. The shell format commands are interpreted by the C or Bourne shells, whichever executes them (more on shells later).
When UNIX was first written, /bin and /usr/bin physically resided on two different disks: /bin being on a smaller faster (more expensive) disk, and /usr/bin on a bigger slower disk. Now, /bin is a symbolic link to /usr/bin: they are essentially the same directory.