What is the difference between white box and grey box testing?

Well, white box testing refers to testing a system with full knowledge and access to all source code and architecture documents. However, grey box testing is testing a system while having at least some knowledge of the internals of a system.

Moreover, the3rd type called black box testing which is testing a system without having specific knowledge to the internal workings of the system, no access to the source code, and no knowledge of the architecture.