I don't think your definitions of "formula" and "function" are correct. The way you've described them will not clarify it for people that don't understand it.
For starters, your definition of a function is not correct. You wrote "A function is a calculation or operation that returns a result". That's actually what a formula is. Moreover, you wrote that a function begins with an "=". Also not true. Formulas begin with an "=", not functions. A formula can contain operators and operands, as you say, but a function is simply one type of operand.
The best way to think of a function is as a kind of pre-written, built-in formula - one that's been given a name (e.g. SUM).
I know I'm being petty and picky, but I used to teach Excel for a living, and I know from experience that it's important to get people to correctly understand the difference between a formula and a function.