If a form has ever come back to you with a note asking for it in .odt, you have met OpenDocument. It is not an obscure format and it is not a broken one. It is an ISO standard, and the reason it turns up in government correspondence is procurement policy rather than technology.
The practical differences
For an ordinary document — headings, paragraphs, a table, some images — .odt and .docx are interchangeable, and converting between them is one clean step in either direction. The differences show up at the edges: tracked changes, comment threads, complex numbering, and anything involving an equation editor.
- Text, headings, lists, tables, images: identical in both directions.
- Tracked changes and comments: survive, but can be reordered.
- Equations: rewritten, and worth checking by eye.
- Macros: do not come across, and you would not want them to.
Which one to send
Send what was asked for. If nothing was asked for and the document is final, send a PDF. If it is not final and somebody needs to edit it, ask which program they use rather than guessing — that one question resolves the format argument entirely.
Worth knowing
Both .odt and .docx are zip archives with XML inside. You can rename one to .zip and look, which is occasionally the fastest way to find out why a file will not open.