In this video on total dual integrality: https://youtu.be/l8YdPRxqlXo?list=PLXsmhnDvpjORcTRFMVF3aUgyYlHsxfhNL&t=798
If the dual has an integral solution, not just an integral value ...
The professor emphasizes that the dual must have an integral solution and not an integral value, saying that it's because this is a specialization and hence is weaker.
What exactly does he mean by making this differentiation between solution and value?
By integral value, he means $y^T b\in\mathbb{Z}$. By integral solution, he means $y\in\mathbb{Z}^m$.