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The most noticeable thing you will find regarding the two ways of running the command is that
Code:
./<executable file>
will run the command within your terminal window and you can't use the terminal till it's complete and control is passed back to the terminal (The prompt re-appears) Yes, the executable file must be within your current directory.
Code:
<executable file> &
will display the PID of the process the command started in the background but you are still able to work with the same terminal.
I thought you might like a slightly less-technical reply.
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