Understanding school rankings...
School rankings by Regent exam indicates the amount of information a student absorbed by the end of a given year. It is used throughout New York State as a measurement tool.
School rankings by SAT score show how well the student has absorbed information for this particular college entrance exam. Many colleges use SAT as one of a handful of screening criteria. The SAT is administered across the nation and compared students from a wider sampling then just NYS students. Think of it as high school graduate's cumulative knowledge as compared to a "per grade" Regents exam.
School rank by Advanced Placement shows how well a student absorbed freshman college work. It also qualifies for college credit if a student gets over a certain score.
If a school has a low Regent but high SAT and AP score, it then can be interpreted as the students choosing (or encouraged) to study for the SAT and AP over getting high scores on their Regents since it will be the SAT & AP that lead to college placement and credit.
Then there is the alternative factor where a high school does not follow the typical standards of measurement. e.g. "School of the Performing Arts", "School of Technology" or Waldorf methods. Then the focus is different and the colleges take this into consideration, often looking towards interviews, portfolios and projects as a measure of the student's ability. Many colleges keep spots open for alternatively educated students in order to round out and diversify.