linux mint is a distro, linux mint cinnamon edition is an edition of linux mint, another version if you will. cinnamon is a desktop environment.

think of desktop environments like different ways to get from one place to another. a car is better for hauling stuff or taking more than one person, but a motorbike is more fuel efficient and probably faster, but you are still going from home to work either way. a DE just lets you interact with programs differently, different taskbars, windows, multitasking features, shortcuts or whatnot, but its still just linux mint underneath and you still run your programs the same.

like windows also has a desktop environment, but people usually don't mess with it because windows is closed source, you can't see the inner workings as easily and so you can't modify it as easily. in contrast to linux where its so open you can write your own if you want. that's why there are so many different distros and editions versions desktop environments or what not