What is the "greasy-greazy line" and the "pail/bucket line"?

These terms designate regions of significant dialect difference in the USA.

"One of our most notable regional distinctions is the "greasy-greazy" line. It is famous among scholars of American dialects for marking a clear division between major dialect regions of the United States. In the North and West, greasy is pronounced with an (s) sound; in the Midlands and South, it is pronounced with a (z). According to the Dictionary of American Regional English, the "greazy" region extends from the deep South to southern parts of New Jersey, Pennsylvania, Ohio, Indiana, and Illinois and all of Missouri, Texas, and New Mexico. The verb grease also follows this pattern, although not the noun grease, which is pronounced with an (s) sound everywhere. A few Southerners also use (z) in blouse. The (z) pronunciation is so stable and so characteristic of Southern dialects that dialect scholars use it to trace the migration of Southern speakers into other dialect areas, such as Colorado, Oregon, and California."

http://www.answers.com/topic/greasy

http://www.pbs.org/speak/seatosea/americanvarieties/pacificnorthwest/