I'm using intimate in its sense of mutual relation rather than the content of discussion, though these aren't fully independent.

Borrowing from the Online Etymological Dictionary, "intimate" meaning "closely acquainted, very familiar", and which comes from the Latin intimus: "inmost, innermost, deepest".

<https://www.etymonline.com/word/intimate>

That is, an intimate relationship or conversation is one in which the participants are both engaging at their deepest and most personal level.

This contrasts strongly with a common experience online and in broadcast media of parasocial relationships.

Tom Scott has an excellent discussion of this in his 2019 video "There Is No Algorithm for Truth", at 33m36s: <https://yewtu.be/watch?v=leX541Dr2rU&t=33m36s>. Well worth watching.

Based on Donald Horton and R. Richard Wohl, "Mass Communication and Para-Social Interaction" (1956): <https://archive.org/details/donald-horton-and-richard-wohl-1...>