A relation is said to be in third normal form if it does not contain partial functional dependency. A relation in the third normal form are said to be stable relation.
A relation is said to be in BCNF if there is no multi valued functional dependency.
The third normal form and BCNF are both normal form that used to relation database normalization in a table.
In third NF in a table if and if only for each of it's functional dependencies.
The BCNF is stronger version of #NF.
Third normal form defines that prime attributes are transitively depend on key or super key and BCNF defines neither prime nor non-prime attribute may not be transitively depend on key and left hand side of all FD's contain keys.If a normal form exists in BCNF it must be in third normal form.
In the third normal form attributes are not belongs to candidate key, it should directly depend on the every candidate key. A table is said to be in BCNF, if each of the dependencies of the A to B that are the non trivial, where as A is the super key.