Meaning: to become known, to become public knowledge Examples: I don't want it to get out that I am leaving. Please don't tell anyone. If this bad news gets out, people will panic and try to run away.
To carry on with something
Meaning: to construct or build something Examples: The people set up camp by the lake. The child was building something with her blocks, so I asked her what she was setting up.
Meaning: to continue without interruption Examples: The discussion ran on for hours. Don't start that book, it runs on for hundreds of pages and never says anything.