Paprika is essentially a form of chilli powder, but a non-straightforward form. It is generally made from a particular form of pepper, known as Capsicum annuum - a form of capsicum. However, some forms may differ from this, as peppers, chillies and capsicums occupy a continuum of related species, and farmers just grow the ones that they have rather than performing biological analyses of the species-types.
Nonetheless, paprika can be broadly categorised into two main forms:
Spanish paprika is made from smoked capsicums, and is generally made from mild peppers, though this can vary. The smoking process imparts a certain complexity, and as such, Spanish paprika is generally regarded as the more flavoursome of the two types.
Hungarian Paprika is made from non-smoked capsicums, and is usually made from hotter varieties. It is more designed to add heat as well as flavour to dishes.
Overall, Paprika differs from chilli powder in that chilli powder offers more heat, whereas paprika is more flavoursome. It has a more "mediterranean" feel and is used to flavour meats and sausages (including chorizo), rather than curries where chilli powder is used.