I don't really know how to talk to "lay people", in any fields.

When studying musicology, I used to say -when talking to someone with no clue about it- "I'm studying musical paleography and philology", to give a hint toward what that's about.
Then, you know, I don't really care about it. Those in need for a musicologist will know how to address me.

As for magic: those who think that "magic" means "magic for kids" will look for "magicians" only when kids are involved, so no problem.
Those who need your services (or do care about your interests) will know exactly what you mean and will ask you more information on their own will

Part of me agrees with your post above, but gets a mental hick up on this phrase.

People may indeed want more magic in their lives (challenge to imagination and acceptance that there inexplicable things in this universe),
but do not "need" a performer for that. If they can't find magic in the world around them they will not find it illusionary skit.
They may want someone to entertain them as a diversion for self-inflicted boredom, but there is no need.

Meanwhile, a person's interest in studying magic may have little to do with any desire/need to entertain others, but most magicians
do focus on the entertainment aspects of the art over the benefits of mental stimulation and appreciation of awe&wonder.

Se, we are looking at a possible marriage of "wants" in which the performer will pretend at magic and the observer will pretend to enjoy it.
The internal effect and affect of the event on both may be far different from what is seen and reported.

You are correct in the important of questions asked rather than relying on assumptions or stereotyped labeling,
but that should work both ways. The lay person may not have the experience to asked the right questions,
and the magician should avoid making assumptions about the potential client because they use the wrong word or can't express their needs/wants properly.

This is why hiding from being called a magician is unwise (opinion). It provides an opportunity to discover or focus on the 'want' while possibly uncovering a 'need'.

A parent seeking enliven a kid's birthday party has options of clown, game-leader, air-filled mega-toys, craft instructor, etc. Why a magician?
Somewhere in the request may be a hidden need of the parent for something lost in childhood or daily life. What is the expectation? How can the performer meet or exceed it?

When I have performed shows for focus age group, I always explore the hidden need and offer some magic Effects for 'the other observers'.
At a kid's party that may be the adult watching from afar. For an Assisted Living Center that means to Social Director and nurses.
For teenage girls' party it may be the brothers watching from the staircase.

As a "professional" it is up to me to ask the right questions. Look for the hidden need rather than the fumbled statement of wants.