A structured and reasoned approach to exploratory testing is termed as Formalized Exploratory Testing. This approach consists of specific tasks, objectives, and deliverables that make it a systematic process.
Using the systematic approach (i.e. the formalize approach) an outline of what to attack first, its scope, the time required to be spent etc is achieved. The approach might be using simple notes to more descriptive charters to some vague scripts. By using the systematic approach the testing can be more organized focusing at the goal to be reached. Thus solving the problem where the pure Exploratory Testing might drift away from the goal.
When we apply Exploratory Planning to Testing, we create Exploratory planning.
The formalized approach used for the Exploratory Testing can vary depending on the various criteria like the resource, time, the knowledge of the application available etc. Depending on these criteria, the approach used to attack the system will also vary. It may involve creating the outlines on the notepad to more sophisticated way by using charters etc.