How is an average mass different from a weighted average mass?

With any element, there are a range of isotopes . . . a weighted average mass is used because there exist different isotopes of that element, each of varying mass.  A weighted average accounts for the fact that the average mass (that may likely be measured from a random sample of the element) will most likely reflect the average mass of the more abundant isotopes.  So the weighted average mass will be most comparable to the more abundant isotopes.

Essentially, average mass is unweighted (each entry has equal weight) while for weighted average mass, each entry has a weighting factor multiplied into it. An example will suffice. Chlorine has two stable isotopes, Cl35 and Cl37. The average mass of these would be 36. However, 75 percent of natural chlorine is Cl35 and 25 percent is Cl37. So the averaged mass is 0.75 x 35 + 0.25 x 37 = 35.5. If you check the Periodic Table, this is the value you see for chlorine.