Great question! This gets to the heart of why quantum teleportation has any value at all.
So, before QM there was already a sense in which you could teleport an object: simply measure its state perfectly and send that information to another location and have them reconstruct that state particle by particle. In principle the new system would be indistinguishable from the original system and you could claim that you've teleported it. Now, with the discovery of quantum mechanics, this process no longer works because there is no way to measure the complete state of a quantum system. For example, you could measure the position of each particle to arbitrary accuracy or you can measure the speed of every particle to arbitrary position, but you can't do both (Heisenberg's uncertainty principle). So, it would seem like one could not construct a perfect replica of a quantum system in a new location by measuring its state in the original position.
The cleverness of quantum teleportation is that you use entanglement to sort of short circuit this limitation. You let entanglement do the heavy lifting to sort of "copy" the state from one location to another and then perform a measurement in the original location to uncover just enough information so that the person in the second location can manipulate its system to reconstruct the original state.
It's sort of like reconstructing the state without actually knowing what that state is.
Now, an interesting side effect of the quantum version is that the first measurement of the original system is necessarily destructive. As such, it's not like you'll end up with two copies of the same thing (which is what would happen in the classical version) so there's no discussion necessary around the distinction between teleportation and cloning. Classically you'd be cloning the system but quantum mechanically you'd really truly be teleporting it (in fact, there's a result in quantum mechanics called "the no cloning theorem" that proves that cloning in QM is impossible).