Yes, that area is part of Karelia.
You could be right that the Russians want the Finnish bit but the Finns talk, probably many years ago, of the Russians trying to do a deal with the Finns whereby they would sell back the bits they already had - when they needed hard currency?
Sadly? for the Finns the price was too high.
If the Russian intention is to go back to the Tsarist borders then you are right and I think that would cause, certainly a cold war type standoff and possibly a confontation - smacks of Germany invading Czechoslovakia.
In simple terms, at the time of the Russian revolution, the whites won in Finland (it was an autonomous part of the Russian empire) and declared independence.