Thinking is a mental process which allows humans to model the world, philosophy is the attempt to understand the world using logic and reason. The world being both the external and the internal, and both the knowable and unknowable.
For an overview of philosophy see our branches of philosophy page, for an introduction to philosophy check out Reason at Work (Amazon). Philosophy includes everything from economic and political philosophies, to the philosophies of emotions and mind, to cosmological and other other metaphysical questions, to the nature of god and religion, to the very nature of what we can know. Given that every subject has a science and philosophy (with the two often merging, such is the case in theoretical physics or mathematics) we have to be careful not to undervalue the practical aspects of this non-science.
Cognitive Artificial Intelligence (AI) is a computer program that can think, learn, and generally mimic human cognition.
The speed and complexity of our thoughts exceed our abilities of language and communication, specifically our ability to convey complex ideas.