For Windows 7/Vista/XP there are three different files at the moment:
flashplayer18pp_hd_install.exe - Opera and Chromium (PPAPI)
flashplayer18ax_hd_install.exe - IE (ActiveX)
flashplayer18_hd_install.exe - Firefox (NPAPI)
These are shim installers which download and install Flash Player silently in the background. The shim installer does not download the MSI installer in your next comment.
There is another location:
Size much bigger: 19 588 096
It seems to work with Firefox and other browsers too.
My question: is the .msi file kind of "global" - and design to work with all browsers?
What does .msi contain? (I guess all plugins above and something more?)
No, it will not work with all browsers. The NPAPI plugin will work with NPAPI browsers (E.G. Firefox), it will not work with IE (which uses ActiveX Control) or PPAPI browsers.
MSI installer contain additional information that is used by software management tools such as SCCM (Microsoft System Center Configuration Management). The MSI installers are used mainly by enterprise customers to deploy Flash Player within their organization (the page where you found the link, Adobe Flash Player Distribution, contains information on licensing the Flash Player for distribution).
Now I see all other links. That helped. Thanks!