The difference is one is a process and the other one is an end result.
Competitions inside of the company are one way for managers to show some progress, but only when you build a culture of people wanting to be competitive towards the competition is when the magic happens.
Many HRs think that by creating competitions inside the organizations, they achieve the result of people rally together and making the organization more competitive. To create a competitive environment, you need to focus on your people and their needs.
Better working conditions, team buildings and salary that satisfy their needs, as well as recognitions towards achieving main milestones is a better way to foster a competitive culture. But rarely company will go that way.
How about you and your company? Do you see more gimmick competitions being introduced, or the environment is naturally more competitive?