Extracting structure and content from invoices
I think extracting relevant details from an invoice in commercial applications certainly involves a lot of high spec algorithms. Maybe you are right that they identify relevant parts first and extract the details afterwards. 

However, my first starting point would be to get all the text from an invoice (e.g. via tesseract). If you have a decent photo, tesseract will be able to OCR the content. The next step would be to identify relevant content, such as payment amount, names, and bank account numbers. This may be possible by hardcoded rules to some extent. Alternatively, one could use NLP-like models to detect certain sequences. With some effort, this should work out well since invoices are relatively structured documents. 

https://pypi.org/project/pytesseract/

https://github.com/tesseract-ocr/tesseract/wiki