With Netbeans, do I seem to have a project listing directories for the rest of the structure (and the IDE to some extent)?
Visual Studio dictates the specific layout of the project, and since the compiler is so tightly integrated into the IDE, there is no real concept of a script assembly. On the contrary, Java does not have such a structure (although certain "best practices" have appeared, such as the presence of the "src" directory for source files, "lib" for libraries, "test" for a test source, etc.) And a build script is usually required tell the compiler that he must find the source files and libraries, which artifacts to produce, as well as the assembly of other tasks (running tests, deploying, creating code metrics, etc.).
In simple cases, the IDE will take care of this for you (if you follow the convention for that particular development environment), but in the end you will probably want to take a look at the build tool to understand what happens behind the scenes. Apache Ant and Apache Maven are both outstanding offers. Ant is very flexible, while Maven is trying to dictate the overall layout. I suggest you study and see what suits.
There is also a degree of separation between the compiler and the IDE. I'm in a situation where I can compile my project just fine, while the IDE tells me that I still have errors
If your code compiles, it is correct. The IDE just acts as a consultant (and will highlight problems besides compiler errors, for example, to warn you about possible code errors or bad practice).
and I guess this is because I have a project installed incorrectly
This is an opportunity, although, as stated above, there are many other explanations.