This isn't an impression I am quoting but rather directly from the AMCAS website. Since AMCAS makes the rules on this, I would consider it the most accurate.
There are two different "systems" overlapping here. Lets see if I can explain it.
AMCAS is an application service that solely administers, verifies, and maintains data/statistics for the members schools of the AAMC. From AMCAS point of view for data and statistics, once you apply one year, the next year you are a reapplicant . I will have to double check this but point but if you submit AMCAS one year and reapply the next, for stats you are a reapplicant.
When you use AMCAS you tell them which schools you want to apply to. From the school's perspective, if and only if you have directed your application via AMCAS to that specific school previously would you be considered a reapplicant at that school.
So if year 1 you apply to 10 schools and get rejected, and the next year you submit to the same 10 schools plus 10 new schools you would be a reapplicant at the repeated 10 schools and a new applicant the new 10.