# difference between Lipschitz on any bounded set and Locally Lipschitz?

Please, what is the difference between the following expressions "Lipschitz on any bounded set" and "Locally Lipschitz"?

The function $\sqrt x$ is locally Lipschitz on $(0,1)$ but is not Lipschitz on the bounded see $(0,1)$. This example is possible because $(0,1)$ is not compact.