What is the difference between thinking and deliberate thinking?

Simply. 

There is the thinking we do when we are driving or sitting at a desk reading documents or taking part in a discussion. However, deliberate thinking means setting aside some time to think with a clearly defined focus.

thinking is casual and common phenomenon, while deliberate thinking is planned and  focussed activity to solve a problem or sometime to remember the past

Purpose.

Deliberate thinking is actually the manifestation of deliberate use of Will Power..

I believe the process of thinking  is a general term refers to human  brain  constant activity,we think all the time about every aspect of life including needs,wants...etc,.

deliberate thinking I believe is the process of innitiating the action to focus on one subject and finding a solution to a specific matter or challenge.

Only thinking is usual but deliberate thinking is to take care of the particulars. 

Thinking is open but deliberate thinking is secured.