1. Web Deploy - If you have IIS on server machine running and configured to receive Web Deploy requests, it will send all requested by IIS files. IIS will immediately start running new web page.
2. Web Deploy Package - If you have IIS on server machine running and configured to receive a Web Deploy Package it will pack your whole web page, and will upload them to server machine. IIS will immediately start running new web page.
3. FTP will upload files to FTP server (can be any OS that handles FTP), but be aware that this is NOT safe and whole upload process can be captured and compromised.
4. File system will deploy all items required for launching a web service, with any method supported by current project configuration, into provided directory on your machine.

Web Deploy: Deploys your app to a local or remote IIS server immediately (one click publishing), assuming you have access and the server is configured properly.

Web Deploy Package: Similar to Web Deploy, but creates a zipped deployment package on the local file system to be deployed later to a local or remote IIS server.

FTP: Copies the required app files to an FTP server. You might use this to deploy your app to the (non-Azure) cloud.

File System: Copies the required app files to the local file system. Useful for testing or if you want more control over how the deployment is done.

The two web deploy methods are smarter than the more old-school FTP/file system approaches. For example, they can apply config file transforms during the deployment, and they are faster because they only transfer changes. They are also more secure.

More info here.