Good question...I think washed leather is treated to be super soft and squishy for that casual look. I cannot find any info on what washed leather means.
This is from wikipedia:
Full-Grain leather, made from the finest raw material, are clean natural hides which have not been sanded to remove imperfections. Only the hair has been removed. The grain remains in its natural state which will allow the best fiber strength, resulting in greater durability. The natural grain also has natural breathability, resulting in greater comfort for clothing. The natural Full-Grain surface will wear better than other leather. Rather than wearing out, it will develop a natural "Patina" and grow more beautiful over time. The finest leather furniture and footwear are made from Full-Grain leather.