We'll be enrolling my 3-year-old in a private gifted school next year for pre-K. He's currently in a Montessori. When asked, I tend to use language like "a better fit." If asked how it's a better fit, I point out non-gifted things that are positive about the school - like small classroom sizes and great teacher/student ratios. Many people in our area know this private school as a gifted-only school, but some do not. If someone googled it, they'd find out fast enough if they really cared. But, I definitely avoid talking about it as a gifted school (even though that is exactly what is, and honestly the reason we are sending our son there).
If a parent were struggling to find a good fit for their own gifted kids, and the giftedness of their child was the primary reason other schools weren't working... Then I'd tell them all about it and not censor myself (as much).
I know it's so hard. I really never discuss milestones or much of what my kid are up to with anyone other than my own mother. In reality, though, anyone that meets the kids knows within moments of meeting them just how different they are. But that doesn't mean they want to hear ME acknowledge that.
