They both are descendants of Old Norse. The differences between these two languages are that Icelandic has ö, while Faroese has ø, and I think Faroese has more borrowed words (especially from Danish and English) than Icelandic. Icelandic is spoken in Iceland, while Faroese is spoken in the Faroe Islands, a dependency of Denmark.
For natives: if I'm wrong, please correct me.
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