When I first was teaching D&D 5e to my group, one of my friends (he mostly had experience with 2e and OSR) kept getting confused every time I asked for a saving throw, because he believed he hadn't written down those stats yet. I realized that he was expecting special saving throw names that were modified by the 6 abilities (rather than using the 6 abilities themselves), because I did not specify clearly enough the new changes to saving throws.
I want to avoid this problem (of confusing older edition concepts with 5e ones that appear/sound superficially similar) the next time I explain the game to a mixed group of people (they will have played with 2e, 3.x, or 4e), without boring them to death by going over every single detail, especially for aspects of the game they already know.
Assuming players will default to knowledge based on previous editions, where applicable (such as "Saving Throws"), unless they have been told how 5e really handles it:
How can I do this better next time? What strategies have you found to be successful?