No, Finlandia is not written by Grieg. This record is a collection of fragments of both Norway and Finland, with Grieg supplying the first, and Sibelius the second. Since Finlandia is widely known and sounds good, it is the title of the record.
Finlandia was written as a covert protest against Russian press control. Sibelius wrote it in 1899, and at the beginning it was known under lots of different names, to circumvent Russian censorship. It is a rallying nationalist piece, speaking of a proud Finish people.
Finlandia is also the sixth and last part of a cycle called Press Celebrations Music Suite, but never released as such. Only in 1998 it was reconstructed and recorded.