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Covariant tensor(rank 2)

A'_ab=(&x_u/&x'_a)(&x_v/&x'_b)A_uv

Where A_uv=(&x_u/&x_p)(&x_u/&x_p)

Where p is a scalar

Contravariant tensor(rank 2)

A'^uv=(&x'^u/&x^a)(&x'^v/&x^b)A^ab

Where A^ab=dx_a dx_b

Metric tensor sometimes g^uv,sometimes g_uv

ds^2=g_uv dx^u dx^v=g^uv dx_u dx_v

What different between them?