Note, there are two parts, one is starting, other is stopping.
Also, these are the ways I know of. There could be others. But these are official GlassFish public interfaces.

Way to start the server              Benefits/limitations

1) asadmin start-domain             - Works with any domain.
                                    - Reads domain.xml for any java-config
                                      data.
                                    - May take longer as 3 processes are
                                      involved in the default case. The
                                      number reduces to 2 with --verbose. With
                                      --verbose, ^C on terminal (On Unix e.g.)
                                      will end the server process.
                                    - Starts any domain on given file system.

2) java -jar glassfish-x.jar        - Starts the VM that server uses, directly.
    (where x is the version)        - You undertake the responsibility of
                                      setting VM parameters on command line.
                                    - If you are invoking it from another
                                      Java process, you get a sub-process
                                      handle(e.g. instance of java.lang.Process)
                                      that you can optionally destroy. You can
                                      also redirect standard process streams.
                                    - Meant for power users.

3) Call embedded API from within    - Meant only for embedded use.
   your desktop/console application - Domain.xml configuration is irrelevant
                                      and is not consulted for Java command 
                                      line options while server starts.
                                    - No VM overhead, uses resources from your
                                      ("embedding") VM.

4) Invoking <install>/bin/startserv - Shortcut for 1) with --verbose. Thus by
                                      default "startserv" would start the
                                      default domain in verbose mode.
                                    - Parametrized to deal with any domain. e.g.
                                      startserv --domaindir /Users/kedar mydom
                                      would start a domain named "mydom" in
                                      folder "/Users/kedar" in verbose mode.
                                    - You can use ^C to stop such a process.

In non-embedded case, recommended way of starting the domain/server is 1),
followed by 4).

Way to stop the server                 Benefits/limitations

1) asadmin stop-domain              - Stops any domain, "domain1" by default.
                                    - Causes System.exit() called in server
                                      since --force is true by default.

2) ^C on a console after            - Easy enough.
   using 1) with --verbose,         - Instant gratification ;) .
   2) or 4) above to start


3) stopserv                         - Does exact opposite of startserv,
                                      parametrized same way.
                                    - Needs another shell to issue the command.

4) http://host:port/stop-domain     - Can be invoked from browser.

5) Using embedded API               - Meant only for embedded case. I don't know
                                      details of it. Ask Byron/Kohsuke/Vivekp.

6) Using MBeans (AMX)               - get DomainRoot MBean, then call domainRoot.executeREST(DomainRoot.STOP_DOMAIN);

In non-embedded case, recommended way is 1), followed by 3) and then 2, 4.