The first defining condition for hearsay under Federal Rules of Evidence 801(c)(1) is that it is a statement which the declarant does not make while testifying at the current trial or hearing. As I understand it, this means that the statement (testimony) "I saw Jones stab Smith" offered by a witness is not hearsay, because the statement is made by the declarant at the current trial. This is why people can testify to what they observed.
But even though the testimony "Jones said 'I stabbed Smith'" would be a statement made by a declarant at the current trial, it also includes the statement "I stabbed Smith", and that statement was not made by the declarant at the current trial. Thus the overall statement introduces a second statement. Assuming that this statement is made at the trial to prove that Jones stabbed Smith, the testimony would therefore be hearsay. Furthermore, if Jones were to testify about himself that “I said that I stabbed Smith”, that too would be hearsay (although that statement too is made by the declarant, it was not made at the current trial).
There are various subsequent exceptions where statements are then positively defined as "not hearsay", which I don’t want to pursue at the moment. My question is whether my characterization of the fundamental definition of hearsay is correct (and if not, why not, with case citations especially appreciated). For the sake of discussion, assume this is somewhere in the US.
(My ultimate goal is to understand "adoptive admissions").