I'm trying to understand how the different parts of a Linux system fit together. My understanding is that Linux is the kernel, while a desktop environment such as GNOME provides the graphical interface and Bash provides a command-line shell. If those components already exist, what does a distribution such as Ubuntu or Mint actually contribute? What makes one distribution different from another?
4 Answers
Different distributions make different choices about what to include and how to manage it. They may use different package managers, software repositories, desktop environments, kernels, default applications, themes, and update policies. Ubuntu also adds its own configuration, installer, support infrastructure, and features such as live kernel patching.
You can think of distributions as different complete bundles built from many of the same projects. Ubuntu, Fedora, Debian, and Mint may share much of their underlying software, but they package, configure, update, and support it differently. The bundle itself, along with the decisions and maintenance behind it, is what makes it a distribution.
There is much more to a working operating system than the kernel, shell, and desktop. Bash depends on libraries such as glibc and readline, while commands like ls, grep, sed, and find are separate programs. A system also needs tools for networking, processes, storage, booting, and starting services, often through components such as coreutils, iproute2, and systemd. A distribution brings all of these pieces together.
A distribution is a collection of software projects assembled into a usable operating system. It includes the kernel, desktop environment, shell, system libraries, utilities, applications, configuration, repositories, and installation tools. The distribution developers choose compatible versions, package everything, test it, provide updates, and distribute it as one system.

Some differences are mostly cosmetic, such as wallpapers and themes, but package management, software versions, defaults, and maintenance policies can affect how the system actually behaves.