What is the difference between the sample average y and the population mean?

When a finite number of samples are drawn from a larger population, the sample mean of that sample, while usually close to the population mean, is not the same thing. A population mean, on the other hand, is a description of pretty much ALL of whatever is being examined.

Example of population: Everyone in the USA

Example of a sample: One person, chosen at random, from each of the 50 states