The meanings are not the same. To go full circle means to come back to the place where you started in some process. To go around in circles means to expend a lot of effort, but accomplish nothing. There are a number of examples I can give where a person could say that they have "come full circle", but still felt that they accomplished something of worth. In some instances, the two phrases might imply a futile effort, but not always.

In case there is any confusion, I wanted to say that that is the perfect explanation! Your examples might be: "The police have been going round and round in circles trying to find convincing evidence, but they just can't find any that will make a conviction stick" - they can't charge anyone because they can't find any evidence, but they have been looking for ages! "I used to work in a supermarket but later became an executive for a multinational company. However, I lost my job in the economic crisis and have gone full circle - I am now back in the supermarket".