A landing page can also be a self-hosted site.
The primary reason why a lot of marketers choose to use services that allow for landing page creation and hosting is because it merely simplies the process for creating multiples.
A self hosted site (the way you're referring to it) is generally a blog, or an informational site. It's objective is usually to educate the prospective customer about your brand and what it has to offer, and even to educate them on some of the topics within the industry.
A landing page can also be referred to as a squeeze page. These pages have no navigation bars, it usually has an offer of some sort, the sole purpose is to get the prospective customer to complete a Call-to-Action (enter their email address, Make a purchase, download an app, etc.). The prospective customer has 2 options, they are to either complete the CTA, or they are to leave.
It gets a little more intricate after that, the landing page can send people through a Funnel of other landing pages that are considered Upsells, Downsells, One Time Offers, etc. all seeking to do the same thing... to get the prospective customer to complete a specific CTA.
You can create landing pages and funnels on a self-hosted site, it just requires a LOT more work and effort.
Let me know if you have any questions!