Difference between 1.nymph and adult 2.Larva, pupa and adult

Nymph is a stage of life cycle of cockroach which has no wings and immature reproductive organs. This nymph metamorphosis into Adult cokroach.

Larva, Pupa and Adult are stages of metamorphosis in Insects. Like in butterfly life cycle larva is the catterpillar which feeds voraciously and later metamorphosis into pupa ( cocoon) which is a dormant stage. Inside pupa the insect develops organs and wings.
Later pupa breaks open to release the butterfly or insect.