Ulysses is somewhat opaque about how your writing is actually stored, so here's what it looks like after a few minutes.
- Ulysses definitely Markdown-like, but it is not just a plain text editor with Markdown highlighting.
- It appears to use its own internal file format.
- By default your "files" are not saved anywhere you can see on your file system. They're either stored within the app itself (details unknown) or on your iCloud drive.