What if the defendant later admits that they did in fact kill the victim. Are they getting away with murder or could there be any other options?

There are other options in the case when defendant admits to the crime (of killing the victim)

Explanation:

In case the defendant accepts to have committed the crime of killing the victim, he can be given a thought of receiving some leniency in the punishment.

The counsel of the concerned defendant can argue in the court of law, that act was in a fit of rage, or haste of anger and was entirely not pre-meditated. He can further arague that feeling guilt of the crime, the defendant admitted to his crime hence he should be subjected to a lenient term.