Most small embedded Linux systems will not use a widely known desktop style Linux distro. Embedded systems developers will tend to select specific components that exactly match the target host, such as bootloaders, kernels, and root filesystems. The application(s) that run on the embedded host will normally be proprietary. The kernel may be heavily customized and include drivers for custom target hardware, and the root filesystem may be completely custom built. On larger embedded hosts, the same may apply, or they may load a full or partial publicly available distro. In those cases, I would expect the spectrum of distros used to be similarly diverse as one would find on desktops and servers.