FreeBSD is a Operating System. Linux is just a Kernel. a "Linux Distribution" is the Linux kernel + GNU Userland + a bunch of Distro-specific other stuff (like package managers and more).
FreeBSD isn't the original BSD, that was 386BSD. FreeBSD's the most popular of the BSDs, but I'm not sure I'd call it the "standard" either. FreeBSD does have a kernel that can be separated from the rest of the OS, as in the case of Debian/kFreeBSD, which pairs the FreeBSD Kernel with a GNU Userland and Debian customizations. FreeBSD's Userland can also be used with a Mach kernel, as is the case with Darwin (the core OS of OSX) - with other Darwin specirfic customizations as well.
Most Linux distro have a no-GUI option, commonly called Text Mode or Headless.
A kernel with nothing else would be extremely useless. Kernels are essentially resource managers, they don't really provide much/any functionality that the end user would want. That stuff is provided by the Userland and additional software.