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The most noticeable thing you will find regarding the two ways of running the command is that
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.
<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.