These two adjectives should be easy to remember because their meanings reflect their roots—hard and heart.
Hardy describes people, and other living things, who are strong and tough—not necessarily having big muscles, but rather being hard to kill, being able to withstand damage and difficult conditions:
Trees are among the most hardy living things, able to live through all kinds of conditions.
Hearty can describe people or things, especially human expressions such as laughter and shouting:
She greeted her friends with a hearty shout.
Hearty means “full of heart” where “heart” means strong positive emotion. Hearty laugh and hearty meal are common expressions, clichés even. Handshakes and hugs are also often described as hearty.