Are they the same ?
Is it possible that one has installed the stand-alone flashplayer(
flashplayer.exe xx.swf works) but can't play the
xx.swf in the browser?
The plug-in is what tells you browser to which application to send that mime type and what kind of data it should expect in return...no, not the same
It's possible, but mainly because the flashplayer plugin exists as a separate program, usually libflashplayer.so. For the browser plugin to work on embedded or phone systems it will need to use the same display renderer as the browser. For Linux based phones, X11 isn't always available so you'd need a custom flashplayer, not the normal Linux one.