@kelunik, manual mode gives you instructions for what to do in order to prove to the CA that you control the domain. You must then follow these instructions in order to change things on your server yourself (typically by running the commands that manual mode instructs you to run). Standalone mode obtains the certificate automatically without additional human intervention.
Manual mode doesn’t require you to run the Let’s Encrypt client as root. It also doesn’t necessarily require you to run the client on the same computer that all of the requested subject names in the cert are pointed at. For all currently supported verification technologies, standalone mode and the other modes will require you to run the client as root.
Standalone mode is so called because it doesn’t require you to have a web server (like Apache or Nginx) running in order to obtain the certificate. It will also work on machines where you’re using web server software that the Let’s Encrypt client isn’t currently integrated with. To use standalone mode, you’ll have to temporarily stop any other software that is listening on TCP port 443, which is used for HTTPS connections.
In terms of the history of the names, standalone mode is contrasted with the earlier ways of using the software that integrate with local web servers (and modify the web servers’ configurations). But standalone mode is still automated. Manual mode is not automated, in the sense that a human administrator has to take additional steps to change something on a server to complete the proof of control for each requested name.
Both manual and standalone modes will give you a certificate file that you can then load into other server software. (We haven’t yet investigated whether we have a practical way for this certificate to be automatically renewed.)