You have one of the potential solutions in your question ;-).
The terms of call and invocation are synonymous and mean the point where you use the name of the function to get it executed. Here a quote in The theory and practice of compiler writing by Tremblay&Sorenson, where they speak about programming language syntax for procedures that return or not values:
For this reason, some language designers have inteoduced a special keyword (e.g. call) to clearly delinate the two types of procedure invocations.
At run time when the function is called, it is executed. Two calls in the source code mean two distinct executions. One call in a loop means n executions. Another term that is also used is activation. Here another quote in the same book, when they speak about run-time control flow, and stack management in the case of a recursive function:
(...) the return from that particular activation of FACTORIAL is the point of invocation within FACTORIAL (...)
(note the wording “point of invocation” to mean the place where the function is called).
Conclusion: In your documentation you should use “execution” exactly as you did in your question. “Activation” could be another alternative, but it is less common than “execution” (except for UML designers that use the term in several diagram to mean the start of execution in some context) and could therefore create some ambiguity. If you do not feel comfortable with “execution” you may consider “execution occurence”. It’s not a formal term bu the “occurence” helps to delineate from the general execution of the software.