If I hear someone ring the doorbell and suspect it is the postman, should I say "That would be the postman" or "That will be the postman"? If both are okay, what is the difference?
"Will" implies certainty, while "would" implies a possibility.
"That will be the postman" tells the listener that you're certain the postman is there. Combined with the future tense, this makes little sense, as there is no guarantee that you can predict the future.
"That would be the postman" tells the listener that you're believing the postman is there. Combined with the future tense, this makes perfect sense, as there is no guarantee that you can predict the future.
In commonly spoken English, this distinction is often lost; but, if you make the distinction you are seen as a better user of English.
Related to this is the difference between "Can you get the door?" and "Would you get the door?" The first one asks about physical ability, while the second one asks if someone is willing to perform the action. There are always people who are physically able to get a door that won't, so better English would have you asking "Would" instead of "Can" when asking for a favor to be performed.
That'll be the postman.
Is a nice natural thing to say. In practice you don't need to say anything. It's not uncommon for people to naturally talk to themselves like this, but it's not something that you need to do. "That'd be the postman" would be fine too. It's not something that you would normally use in an un-contracted form. Using "would" might indicate greater certainty than "will".
I don't want to overanalyse this. But if you do then see Sematics of epistemic modals