Parental Control are the such features which let the parent to control the content their child may access or view on mobile, comptuer etc. Parents under Parental Control may restrict access of certain kind of contents, applications, games, programs etc. Spy applications generally comes with features of Parental Control. Generally you will find two kind of spy and monitoring applicaitons on internet.
One with Parental Control features in which parent can restrict things on their mobile devices like certain apps, websites, games etc. In these kind of application child known that there is Parental Control Application installed on their phone. In this case child acts in knowledge that his actions are being watched.
Second type of Parental Control applications are kind of Parental Supervision. In which Parent supervise and monitor childs activities and do not have any option to restrict them, such apps could be stealth in which child do not know that he is being watched. These apps provide more detailed state of child actions as they act freely without knowing that they are being watched one of such app is SpyBrad which can be turned to stealth and it will only let you supervise the activities without any restriction or access control.