Look no further than State v. Barbero, 297 Or.App. 372 (2019). An admission is a statement made for some purpose other than to acknowledge guilt. A confession is an acknowledgement of guilt made by a person after an offense has been committed.
For example, “It’s true I was at the house the day poor Fluffy was incinerated, your Honor, but I assure you I did not smell a thing” is an admission.
“Ok, fine, I did it! I shoved the cat in the oven on purpose!” is a confession.
The distinction is legally relevant.
A confession alone is not sufficient to support a conviction for a crime. There must be some additional evidence, other than the confession, from which you may draw an inference that tends to establish or prove that a crime has been committed. When the state presents evidence of a confession at trial, the defense is entitled to a jury instruction about that. When the state presents evidence of an admission, however, the instruction is not given.
Fun fact: in theory, an admission can corroborate a confession. So a person’s statements to the police, standing alone, can support a conviction, at least in theory.