Perhaps you have some misbehaving software, but I've never seen /usr/share/bin, or /usr/local/share/bin or a lib directory in either of those locations. I just checked FreeBSD boxes (which, admittedly, follow their own standards closely), and a Redhat box.

var is a directory which may be found under /usr or /usr/local, but won't contain a local directory.

Think of it as 3 roots: / is required for boot, /usr is stuff maintained by an administrator (say, company wide), /usr/local is where files installed by local users go. Within each of these 3 roots, you'll have some subset of bin, etc, lib, libexec, sbin, and var. The root directory has some additional singleton directories which don't make sense in the other directories: dev, root, mnt, boot, proc, rescue.