I'm not really a VC. There's no specific name yet for what YC does, but it's closer to angel investing than VC. VCs are fund managers. That makes life very different for them.
I think the distinction here is that the YC partners are investing their own money and the VC are funded mainly by limited partners. In the case of Sequoia, Harvard is a huge limited partner. Though I heard there was a dispute between them because Harvard only wanted to invest in Sequoia's US branch and not the foreign ones. I'm not sure how it was resolved.