While setting up this forum some of our group asked about the phrase Neo-Quenya, being unaware of it. I have therefore made a summary of the discussion which followed, as other new learners of the Eldarin Tongues may find it helpful.
As to what it is, - Neo-Quenya is when a word is needed for which Tolkien has not provided any help of any kind at all. Those who know how to do it go through all the early material such as the Qenya Lexicon, and the Etymologies, and find, or perhaps create Roots which might possibly develop into the required word. Then they trace all the changes through the Ages such as s > z > r and finally create a previously non-existent Quenya word. Helge does it quite a lot when he's translating from the Bible - and has in fact just announced a "Neo-Quenya Translation" of part of Luke this last week.
The difference between a *word and a Neo-Quenya word is that it has a far more tenuous history. Words with an * may be nouns which have been created from a previously attested verb, for instance, or the other way round. They may be words made by taking two attested words, prefixes, or whatever, and putting them together as was done with Alatúlë. Ala- is a prefix attested in PE17, and means "well". The example there is alaquenta "Well said". tul is the verb stem for "come". If I use them together in the correct way I create a *word, but not a Neo-Quenya word. *Words have a word, a stem, or a root from which other words have already developed, and from which this word is created. In notes it is easy to explain a *word, as I did, but Neo-Quenya is more difficult and much more troublesome in that it requires the creator to guess at what Tolkien might have made the language do, and so it does tend to divide opinion.
Whether anyone does such a thing with Sindarin, I really don't know. I've never seen or heard the term Neo-Sindarin used, so my guess is that it doesn't exist. . . . . . Unless David Salo has done a little of that. But, the real problem with his book is that he doesn't give the references and etymologies for the words in his lists.
Helge's lists are an immaculate example, because you know at once that this word came from the second version of the poem Markirya, that word only appears in Firiel's Song, and the third word is from Lost Tales 1. This, for instance, makes it easy to avoid words which might be far too early to fit into something you are writing which is of the Third Age.
With David's Sindarin lists, we are unable to make any judgement of our own, because we lack that information. I believe that Hisweloke is better on that. Dragon Flame had a separate section for newly created words - but who used them, if anyone, I can't tell you.