"Mean", used on its own, always means the sum of the data (with any repetitions) divided by the number of data. Thus the mean of {1,3,4,4}
is {1+3+4+4)/4 = 3. This is also sometimes called the "arithmetic mean."

You sometimes see references to quantities such as "geometric mean" (for N data, this is the Nth root of their product), "harmonic mean", etc. These are different.

"Average" most usually applies to the arithmetic mean but can also be used to refer to the median (middle element after that data are ranked) or mode (most common value.)

Good Hunting!
Robert