What is the difference between Eikon Data API and Eikon Datastream Web Services?

Historically they originate from distinct companies that used to be separate. They provide access to distinct and largely complimentary data sets, although there's some overlap between the two. Eikon Data APIs are available only with an Eikon subscription. Any data retrieved using Eikon subscription is licensed for use by individual user only. Access to Datastream Web Services may be purchased with an enterprise licence.