$path is a shell variable and $PATH is an environment variable.
The shell keeps some shell variables (such as user, term and path) in sync with their environment variable equivalents (USER, TERM, PATH).
The difference between shell and environment variables is that environment variables are available to programmes (like shell scripts) run from the shell, ie: they are "exported". Shell variables are not.
Shell variables are set with "set" and environment variables are set with "setenv".
Suffice to say, $PATH is delimited with : and $path with a space.