Those concepts are quite fuzzy.
Some people consider that the operating system is only the kernel, a rather
strange definition because you do nothing with only a kernel, so the system
is not "operating" imho. Others consider that all programs, from the kernel
up to specialized applications, that can work alongside each other are an
operating system.
GNU/Linux distributions ship the GNU/Linux operating system seen in a
maximalist way. They can differently manage the programs (there are
different package managers), ship with different defaults (for example
different desktop environments), even have slightly different system files,
etc.
Everyone seems to agree that a desktop environment is a set of complementary
*graphical* programs (so a "desktop environment" definitely differ from an
"operating system") meant to work together and having similar interfaces (in
particular using a same graphical toolkit). But again some people have a
minimalist definition (only the window manager and maybe a file browser),
whereas others will consider that a desktop manager should include up to
specialized applications.
