As per Lawkidunya, here are some notes on the difference between admission and confession:

An admission is a general acknowledgement of something, while a confession is a specific admission of guilt or wrongdoing.
An admission can be made in a variety of situations and contexts, while a confession is typically made in the context of admitting guilt or responsibility for a particular act or crime.
Admissions can be made voluntarily or involuntarily, while confessions are typically made voluntarily, as they involve admitting to something that is wrong or illegal.
Admissions and confessions can both have legal consequences, depending on the context in which they are made and the nature of the act or crime being admitted or confessed to.
I hope this helps! Let me know if you have any other questions.