There are public API nodes (such as this.piston.rocks) that run the same database as steemit.com (technically, that database is a blockchain). That said, you can

• use steemit.com and their semi-public API
• connect to this.piston.rocks and use that one
• or deploy your own node and use that one

Technically, there is a way for public APIs to profit from offering a public API node and that is: People are asking for the latest posts in a category with a certain sorting, but no one prevents the API provider to put their own posts higher in the ranking. No one actually even prevents them to give your wrong data. That said, you shouldn't trust any public API unless you trust the operator but on the other hand, the API provider can use it to monetize their public api service.
This of this as a google ranking. If you get the posts from steemit.com, you will see their ranking while when you use another service, you will see another ranking (potentially added extra posts to fund their server) .. the only way to get a neutral picture is to use your own server or maybe pay for a neutral party to provide a neutral point of view.

As a note, this.piston.rocks currently provides the most neutral point of view there is but that might, or might not change ..