Discretion refers to the 'choice' whether or not to do something. There are two main ones we study in legal. Judicial discretion involves the judge having an input into what sentence the offender will receive (please note that this discretion is limited by statutes, mandatory sentencing and maximum penalties) Police discretion refers to the decision made by the police whether to arrest, not arrest, whether to enforce the law, not enforce the law, etc. The reason that this exists is that sometimes there are mitigating circumstances. For example, the police may not fine a man travelling over the speed limit if he is rushing his pregnant wife to hospital. However, if the person was over the limit in a hurry to get to a tea party then they may be fined. This involves the police's opinion or 'discretion'
Truth in sentencing refers refers to the actual time an offender spends in gaol for their offence. This was introduced under the Sentencing (sentencing Procedures) Act 1999 (NSW) . Basically what that legislation is intended to do is ensure that the sentence handed down is the sentence served by the offender (ie. they cannot get out early)