********** NOT A TEACHER **********
Hello, Mr. X.
(1) I found your question and the posters' answers most
interesting and helpful.
(2) May I suggest that we can all agree to call would a modal?
(Then we need not debate the word conditional.)
(3) I found something in Mr. L. G. Alexander's highly respected
Longman English Grammar that might (!) apply to your question:
We often use would in place of the simple present tense when we
want to sound less definite.
Therefore, MAYBE (!!!) we can analyze your examples this way:
(Two people are speaking) "I am going to bring the contract to your
office on Friday. That is fine." = definite.
"I am going to bring the contract to your office on Friday. That would
be fine." = less definite.
Thank you
I disagree somewhat with Parser's example, but only in part. The original question asked the difference between will/would in the question, "Will/Would you be angry?." The use of modal "will" is being used with
epistemic modality, which is the likeliness of a conclusion based on the speaker's deductions. Parser's sentence "That would be fine" has little to do with likeliness of a conclusion but of the speaker's requirements or approval,
root modality.
The correct explanation, I believe, is the epistemic interpretation where present and past tenses of "will" express
distance from reality. In other words,
1) "Will you be angry?" expresses a future state where the speaker is more direct in his question and expecting a clear and precise answer.
2) "Would you be angry?" expresses a hypothetical state where the speaker is asking without committing him/herself to the situation.
EXAMPLE
Will you take courses in linguistics (this semester) ?
Would you (ever) take courses in linguistics (if you went to college)?
This is from Yule's "Explaining English Grammar"
I hope this helps.