They're not the same thing. DBPedia is trying to extract structured information from the existing versions of Wikipedia, which are segregated by language and licensed under CC-by-sa. Wikidata is a newer project focused on providing high-quality structured data from scratch (labeled in any natural language), with a CC-0 license that's as close as legally possible to releasing them into the public domain.

DBPedia is extracting data from infoboxes in Wikipedia, but increasingly Wikidata is the source of the data in the infoboxes.

They overlap. Wikidata uses generated URIs for entities, properties, etc. that are not human readable readable; they can be resolved by hovering the mouse cursor on the SPARQL endpoint web app or add a pattern to get the label for these URIs.

Many of the Knowledge Graph people who I have worked with clearly prefer Wikidata but I am in the other camp: I find it so much easier using the human-readable meaningful URIs for entities, properties, etc. in DBPedia. Yesterday I wrote SPARQL queries for both DBPedia and Wikipedia.