Programmatic refers to the automated bidding and placement of ads in real time auctions done over a DSP. It can be done for audio but would take the listener out of the experience as the ad is built prior to the recording.

Native advertising is when the creative is in the same manner of the content. On a website, the ad would have the same formatting as the other articles on the page. In audio, it's currently being done by having the host read a loose script with keywords/phrases and tie in their personal experience with the product--making it seem like its part of the program.