Prince 2 is a large methodology since it includes in its remit the management of large projects as well as smaller ones, but it is fully adjustable to meet the needs of specific projects, whether straightforward or highly specialised, very large or very small.
PMBOK stands for the Project Management Body of Knowledge is published to identify that subset of the project management body of knowledge, that is generally recognized as good practices. It gives a general overview as opposed to an exhaustive description. Best practice does not mean that the knowledge described should always be applied uniformly in all projects. The project team is responsible for determining what is appropriate for any given project.
If PRINCE2 is popular in Europe, PMBOK is popular in the U.S and the rest of the world. PMBOK is developed by the PMI (Project management institute), which is a non profit organization, which makes and spend lot of money, with head quarters in the U.S and chapters spread across the globe.
PrinceLite is a process that integrates the software engineering process with the project governance process. PrinceLite is a project delivery methodology; it is not a project management method. The main point of PrinceLite is that it is orientated around the business community; it serves the project sponsors (people who pay the IT bill).
PrinceLite is defined specifically to allow you to deliver IT projects. It is of no use for construction or civil engineering.
Prince2 Lite is a tailored version of Prince2. In other words a lite version of Prince2 with a lite business case and lite documentation. PRINCE2 Lite is a simplified adaptation for private sector businesses.
For smaller organisations handling smaller projects, PRINCE2 is too complex and they develop their own simplified versions. These smaller versions are known as PRINCE2 Lite and occasionally called PINO (Prince2 In Name Only) too.