I think most people are able to understand if we say that the wound will "close over". If we start with the analogies that infer that there are similarities then we have to start over again.
When I was out on lawns and a client would use the word I would correct right away "trees don't heal..."
Healing, haircut, tree surgeon... these things that support misconseptions should not be used.
I'm not of the crowd that wants to differenciate between trim and prune, vigor and vitality. These are things that can communicate things between proffesionals.
I look in the dictionary and heal says "restor health and soundness" with a tree the defect will always be there and may cause problems in the future; fissures, cracks and such. So if we say new wood will close over the defect, we don't imply that it is on the same level as a cut to our skin.
I've talked to a number of people that have had a tree person tell them "It'll heal" then I need to explain why ther is decay and slime flux, ect...
To sum the rambling rant up. If we are, as an industry, going to say "Trees don't heal." We need to be on the same page.