Silly of me to have asked the question in the first place then? I'm aware of many differences between distributions. Still, I wouldn't hasten to claim that the kernel is the only similarity between many or even most distros.
Most distributions are GNU/Linux -- ie, they use the GNU userland tools (gcc, bash, coreutils, sometimes Gnome) and the Linux kernel. GNU/Linux is the most popular OS based on the Linux kernel, but there are others. Android and Chrome are two examples of non-GNU operating systems based on Linux.
Silly of me to have asked the question in the first place then? I'm aware of many differences between distributions. Still, I wouldn't hasten to claim that the kernel is the only similarity between many or even most distros.