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

Gray is trash and the other