Well, how I use them is -

I use a 'function' when talking about something specific about a product or unit (i.e. the function of the PTZ button is to access the settings of the Pan-Tilt-Zoom camera in the following ways ... ).

I use 'functionality' or 'functionalities' when describing a broad range of things on one page, without going into detail. So, as a broad overview of an entire product (i.e. on a page titled 'MODEL #### FUNCTIONALITIES' and a bullet list of some of things that I would like to highlight about the unit.) I also often use 'features' instead of 'functionality' though.

So, something like --

Model ## Functionalities Include:
- Record up to ### hours of real time data
- Motion, Alarm, and Scheduled Recording Types
- Backup of data to USB memory stick or portable HDD

And later into it I would describe how each of the 'functions' works indepth.

I don't know if that helps or makes it more confusing -- i think that using 'functionality' is more of a marketing spin on things though