My vague recollection of the SAT and ACT was that they were designed to test your ability to perform certain cognitive tasks, but didn't test whether you had any particular knowledge. There may have been exceptions on grammar questions, but I think that in the math section, you were given any formulas you might need -- whereas AP tests test knowledge extensively.
There may be a point at which you've taken so many test SAT/ACTs that, for lack of a better analogy, you've strengthened those cognitive muscles enough for it to make a difference, but cramming seems like an obviously ineffective way to handle this. AP tests, on the other hand, have a limited scope of facts for you to produce on command.
There was definitely a vocabulary component to the version of the SAT that I took (in the late Nineties). I seem to recall hearing that a later version of the test had dropped that, though, probably over cultural bias concerns.
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