2nd normal form seems to relate to composite keys whereas 3rd normal form relates to primary keys.

2nd normal form - there's a composite key and all fields in the table must relate to both of the composite key fields. If something doesn't relate then it should be refactored into another table.

3rd normal form - everything has to be dependent on the primary key - so I'm guessing that in 3rd normal form there's only 1 key rather than in 2nd normal form where there can be composite keys?