Sure,
Welcome Isabelle (What a nice name!)
I think of precocious as doing stuff earlier than expected.
as in: Precocious little Joey was reading Harry Potter in Kindergarden.
I don't think it implies that Joey will end up to be a better reader than kids who read Harry Potter at the regular age, just that Joey reached that landmark sooner.
Gifted is a word that has many different meanings, but I list it as 'having learning needs that are different enough from their agemates that they are unlikey to have their learning needs met in an unmodified regular classroom.' Gifted kids are often ready to learn material that is usually given to older kids, and they may be capable of learning it more quickly, or with more abstract depth than the older kids.
Dr. Deb Ruf has studies 200 families to tease out the connection between precocious and gifted, and reports on her finding in 'Losing our Minds, Gifted Children left behind.' What I have seen is that, as preschoolers, some gifted children are precosious in talking, reading, math and abstract thought, and some gifted children are not. At some point a gifted child would have to be preforming at the level one would expect of an older child or adult, or you wouldn't know that they were gifted, yes?
This leaves out musically gifted, or artistically gifted.
