Positive thought is the first step to put forth something once the Conscious Mind has conceived the idea of a desired deed. A thought is like blue print before the task is accomplished, every deed is done twice once in the Mind and then practically. Positive thoughts transforms into belief in ones Mind through autosuggestion, sending a clear mental picture of the desired deed to the Subconscious Mind.
Right thoughts are spiritual process carried out by the Intellect. In the spiritual mind our desired deed is transferred to Intelligence. Intelligence will deliver to our Subconscious Mind the knowledge necessary to accomplish the deed. Subconscious Mind does not think, it just responds to the thoughts that it receives from the Conscious Mind. Our Subconscious mind manifests to us anything that we ask for, whether it is good or bad. Therefore, we must direct it correctly through Right thinking.
An incident will illustrate the difference between Positive Thinking and Right Thinking:
It so happened that a group of friends were traveling in a bus to a hill station on a bright sunny day and the bus was going up the hill. The sight of the valley down was enchanting and one person asked the driver to stop the bus as he feels the beauty of the nature has to be captured in his camera. The person gets down the bus and goes to some distance when a big boulder came rolling down the hill and crushed the bus. His entire group of friends and the driver of the bus were killed. If the person or any of his family members think and thank his stars for being saved because he was lucky to be out of the bus, maybe it can be Positive thinking. But the fact or Right thinking is that the big boulder came crushing on the bus because the bus had stopped there at the moment because of him, had he not asked the driver to stop, the bus was traveling and maybe nothing like this would have happened.Let us not go into the logics of Karma here.
Positive thoughts take only the willingness and desire to act and think better in expectation of a joyful mood, while Right thoughts take full commitment to wellness and is inclined more to practice of the Truth.