The difference between will and would is that will describes something that is likely and would is something more hypothetical or imaginary. It works the same on conditionals as in other phrases:

• I'll make some supper;
  • I'm hungry.
  • but I'm not hungry.
• If I went to the bakery;
  • I would buy a cake.
  • I wouldn't buy a cake.

If we speak of something in the past that would have happened we are speaking of a past participle which is used to express something imaginary in the past.

Both would and will are used to ask someone to do something. Would however is a little more polite in such situations.