Part of what makes comparing gifted-program experiences confusing is that there was never one program. There were, and are, at least half a dozen overlapping labels used across different states and districts, each with its own history and criteria. Here is a plain map of the terrain.
Common in California and several other states, GATE typically refers to identification and services, often enrichment-based, for students identified through a combination of testing, teacher referral, and portfolio review, usually beginning in elementary school.
Used widely in the Pacific Northwest and Midwest, TAG generally describes a similar identification-and-services model to GATE, with the specific criteria and delivery format set at the state or district level rather than nationally.
Magnet schools or magnet programs are a distinct model: a school (or a program within a school) built around a specific theme or accelerated curriculum, and open to students district-wide, often through an application or lottery process rather than solely a gifted-identification test. Not every magnet program is a gifted program, and not every gifted program is a magnet.
Typically found at the secondary level, honors courses offer an accelerated version of a standard course, usually without requiring formal gifted identification — access is often based on prior grades, teacher recommendation, or placement testing specific to that subject.
AP courses, run through the College Board, offer college-level curriculum and a standardized exam that can earn college credit. AP is generally open to any student willing to take the course, though schools vary in how much they gatekeep enrollment.
These are two different service models, often confused with each other. Enrichment means going deeper or broader within a grade level (extra projects, different material, more complexity). Acceleration means moving faster through the standard sequence (grade-skipping, subject acceleration, early college credit). Research from the Davidson Institute and others generally finds acceleration to be one of the most effective, and most under-used, interventions for highly gifted students — often avoided due to social concerns rather than academic ones.