The key difference between DX API v1 and Constellation DX API is that v1 is built to expose Pega processes that were built on section-based UIs (using UI-Kit and Theme Cosmos) and Constellation DX API is built to operate on top of newer applications that were built using View-based UIs.  Constellation DX API is also a more optimized API, with additional capabilities and a streamlined call sequence when compared with DX API v1. See https://docs-previous.pega.com/pega-digital-experience-dx-api-overview/87/differences-between-dx-api-v1-and-dx-api-v2 for full details of these differences.

Pega 8.3 is the earliest Pega version that supports DX API v1. Constellation DX API was first seen as a preview release in Pega 8.5, and was made Generally Available with Pega 8.7.  Pega always recommends that customers maintain a regular upgrade cadence to make sure that they can take advantage of new features in the latest versions of the platform.

Pega uses Constellation DX API to power Constellation.  This is exactly the same API that we provide to our customers and partners.  More than that, the ConstellationJS engine that sits between DX API and the Constellation UI layer is also made available to customers through our SDKs, meaning that you can take full advantage of Constellation and build Pega-driven user experiences in your own front-ends without having to consume the DX API directly.