Two of the questions my teacher put on the review sheet for our Acid/Base test are

1) what is the characteristic property of a buffer solution?
and 2) what does a buffer solution contain?

i think a buffer solution contains a weak acid and its conjugate base or a weak base and its conjugate acid but what is the difference between these two questions?

are the characteristic properties of a buffer solution different from what a buffer solution contains?

Yes. You answered #2 and it's a VERY good answer. The characteristic property of a buffered (I don't like to see them called buffer solution--they are "buffered" solution)===

A buffered solution resists a change in pH. To expand, if one adds a strong acid to a non-buffered solution (such as adding HCl), the pH changes dramatically. But if the same amount of HCl is added to a buffered solution, the pH changes but nonly slightly. The same for a strong base. Add a strong base, such s NaOH, to a buffered solution and the pH changes only slightly. Do you know why they work that way? From your definition, lets say we have an acetic acid/ sodium acetate buffered solution.

Here they are.
CH3COOH
CH3COONa.

If we add NaOH, it is neutralized by the CH3COOH, forming more CH3COONa. The end result is that we have transformed a strong base into a the salt. So we have a little more salt (the base) and a little less acid and the pH changes slightly.
If we add a strong acid, such as HCl, the H^+ immediately gets tied up with the acetate, like this,
CH3COO^- + H^+ ==> CH3COOH.
The net result is that we have transformed a strong acid into a weak one. The acid concn increases a little, the base concn(acetate) decreases slightly, and the pH changes only slightly.

You're on the right track! A buffer solution indeed contains a weak acid and its conjugate base, or a weak base and its conjugate acid. However, there is a distinction between the two questions.

The first question, "What is the characteristic property of a buffer solution?" is asking about the unique property or behavior that differentiates a buffer solution from other types of solutions. In general, the characteristic property of a buffer solution is that it has the ability to resist changes in pH when small amounts of acid or base are added.

On the other hand, the second question, "What does a buffer solution contain?" is asking specifically about the components or ingredients that make up a buffer solution. As mentioned earlier, a buffer solution consists of a weak acid and its conjugate base, or a weak base and its conjugate acid.

To recap, the characteristic property of a buffer solution refers to its ability to resist changes in pH, while the contents of a buffer solution refer to the specific components it contains.