diffrence between single user and verbose mode

Single User mode loads only the command line and the parts of the system necessary to use it.

Verbose mode displays details about the system processes while it's starting up. There isn't an operational difference.

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Single User Mode is running as 'root' which is about as powerful as you can get on a Unix based system. So you are way beyond 'Admin' 🙂

Single User Mode also has a very limited user interface. Or more specifically, it is a Unix command line.

Be very careful when working in Single User Mode as there is not much to stop you from destroying your data.

Verbose is just a very noisy way to startup the system. Generally these are the messages that are normally put into the /var/log/system.log file, but now they are also displayed on the monitor.