According to the PMI, adaptive project life cycles are those that are designed to respond to change and uncertainty, primarily with stakeholder involvement throughout the effort. They are also characterized by short iterations. The overall project requirements are uncovered by doing the work and reviewing the evolving product with stakeholders to make sure that the work being done meets their needs.
However, the PMI also states that a "detailed scope is defined and approved before the state of an iteration", which is not a requirement of agile methods. Some agile methods, such as Scrum, focus on goals instead of work output and readily accept changes to scope that do not endanger the goal.
There's a very close, but not an exact, relationship between adaptive and agile methods.
No agile methods can be predictive. Predictive usually refers to the overall project. Since agile (and the PMI's adaptive) methodologies are about uncovering the requirements as the effort goes on, it is not possible to predict effort, schedule, or budget in advance. There's no effort to attempt to detail too many requirements upfront that would enable the prediction of the effort.