I guess you're looking for a sound effect equivalent to a herbarium or a wine aroma dictionary.
However, the result of an effect only means something when applied to a sound source. So whereas everybody can see what a dandelion looks like or what elder flowers smell like, the ability to understand and separate the original sound from the sound with a particular effect applied might require training and experience with sound production.
I think hands-on demonstration on something the client already knows, i.e. the actual material you are working on together works much better. They might not be able to tell what the effect does, but they can pitch in with whether they like the result or not. I've worked on projects in the past where I would make several alternative mixes to gauge reactions and gather hints for further directions to go down.
I'm wondering why you would be discussing effects with a client up front. Maybe you have good reasons for doing so, but I'm thinking that referencing well-known songs as you mention yourself works pretty well. Again, without knowing your specific context, I would think discussing styles and artistic directions rather than particular effects would be a much better goal and mind set for both of you when laying out a potential project with a client.