To expand on this just a little... the fundamental difference between "paid" and "organic" would be that the first one is a paid campaign (Facebook, Twitter, Google, etc all have mechanism by which to promote your own content on the platform for an extra cost)... these should be appended with a campaign code that specifically indicates this as being paid.
Organic on the other hand would be content that is crawled and shows up in the normal search results on Google, or content that has been shared by users on social media, or shared by internal staff to their personal social media pages, etc... no one is paying to promote these links... they are just shared to the platform, and seen by users who get those feeds (or who see the feeds for the re-post/re-tweet/etc).
This is why people often have Paid and Organic (or Natural) Search, as well as Paid and Organic Social Media, etc... since users can come from these sources in different contexts (paid and not paid campaigns), but your business definitely wants to watch their paid campaigns a lot closer to see if the money they are spending to drive traffic is worth it.