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Finnair generally use a fairly standard "universal" 2/3 prong power socket that will accept (at least) plugs with a US or European style plug, with power at 110 volts.
Depending on the specific plane it may also have the even-more-universal socket that will also take UK, Australian, etc, plugs - however I would not recommend relying on that as not all planes have them.
If your plug is non-US/UK, then you will likely need to use an adapter to connect it.
The "no adapter is required" comment relates to the original in-air power sockets which which required an "adapter" (basically another power pack) in order to use them with most equipment - they are saying that no such adapter is required on their planes.