Hope in Christ is not the same thing as what is known as positive thinking.
To begin with we need to define what positive thinking is. As it is typically used, positive thinking is focusing on the positive to bring about a positive result. What is implicit in this ideology is that we have the power to make things happen by simply just willing it.
There are some problems with this. To begin with it presumes that we have the power to actually create and guarantee a good future. While it can be said that we can influence the future through our attitudes and actions, it is only by either the enablement or permission of God. The "preacher" in Ecclesiastes (Ecc. 9:11), from a secular perspective, says that the swift, the warrior, the wise or those of great ability are all subject to time and chance. In other words, they are all subject to things that are outside of their control. We don't have to look very far in our own lives to be reminded of the times when things didn't work out no matter how much we believed that they would. When we embrace positive thinking we are trusting in ourselves and in what we deem is good.
Another problem with the ideology of positive thinking has to do with what happens when two people want the same thing of which there is only one of? They both totally believe that they will get what they want but since there is only one of them, it is impossible to satisfy both of them … for example take the case of one job with two applicants. Or there is sports … only one team can win.
From a Biblical perspective God is the only One Who defines the future and the One Who brings the future into the present. As we trust in God we are recognizing and trust the One Who does control all things. Look at some of these passages to see what they say about God's sovereignty (Prov. 16:33, Job 42:2, Isa 46:9-10.)
When we hope in Christ we are placing our trust in Christ in that His work on the cross for us is both sufficient and finished. We are also trusting that God will work His perfect will in our lives. We are trusting more in a Person rather than a particular outcome. When we embrace Biblical faith, we trust God and that He is working His best in our lives. Instead of trusting ourselves we are trusting the God of the universe Who has shown His love for us through His Son, Jesus Christ (Romans 8.)
So positive thinking and hoping in Christ are not the same thing.