I've had this discussion way too many times with people who convolute these three different things, and then mis-label them. Causing even more confusion.
Yesterday, my ISP link to the house went down while I was gone. My wife tried using the new WLAN Pros Toolbox app's 'Check my Connection' and then called me to complain that, "Your app is broken, it says I have great Wi-Fi but it can't find the internet".
When I got home and did some tests, the link to the ISP was truly down, and I have to spend time with their tech support to get it back up.
In trying to explain what happened to my wife... I came up with this graphic. Explaining why her laptop couldn't get to the internet, but her phone was extremely slow. (We have terrible cell signal in our house)
As soon as the ISP re-connected our fiber link - magically my wife's Wi-Fi was all better. (Even though she had great 'Wi-Fi' the entire time the ISP was down)
What kinds of analogies do you use to explain the differences between Wi-Fi, Cellular, and Internet to your family and customers?