Posts that start with "Launch HN" get placed on the front page similarly to how job ads do. These are the two formal things that HN gives back to YC in exchange for funding it: https://hn.algolia.com/?sort=byDate&dateRange=all&type=comme.... The difference is that job ads can't be upvoted and decline in rank as a function of time, while Launch HNs can be upvoted and get ranked like regular stories after the initial placement.

Posts by YC startups after their initial launch don't get any special treatment. If a submission doesn't say "Launch HN", it's subject to the same rules as everything else.

Edit: HN also displays YC alumni names in orange to other YC alumni.