As the title says.

I'm having a really hard time trying to understand what the differences between a desktop environment and a window manager are?

There are basically three layers that can be included in the Linux desktop:

X Windows – This is the foundation that allows for graphic elements to be drawn on the display. X Windows builds the primitive framework that allows moving of windows, interactions with keyboard and mouse, and draws windows. This is required for any graphical desktop.

Window Manager – The Window Manager is the piece of the puzzle that controls the placement and appearance of windows. Window Managers include: Enlightenment, Afterstep, FVWM, Fluxbox, IceWM, etc. Requires X Windows but not a desktop environment.

Desktop Environment – This is where it begins to get a little fuzzy for some. A Desktop Environment includes a Window Manager but builds upon it. The Desktop Environment typically is a far more fully integrated system than a Window Manager. Requires both X Windows and a Window Manager.