What's the difference between 떨다 and 털다?

ANSWER: One means "to shake," and the other means "to shake off" or "to shake out."

In Korean, how do you say, "Flick ashes from a cigarette"? Is it A or B?

A: 담뱃재를 떨다.
B: 담뱃재를 털다.

My dictionary lists both, but I have read that the correct answer is A, which is why Koreans refer to an "ashtray" as a 재떨이, not a 재털이. 재 is the Korean word for "ash"; 떨 comes from 떨다, which means "to shake off" or "to flick off"; and 이 is a suffix that means "thing," so 재떨이 literally translates as "a thing for flicking off ashes."

This morning I came across the following Korean sentence and suddenly became interested in the Korean verb 떨다.

"가족들이 모여 대추를 떨다."

Does the above sentence translate as A) "Families gathered to shake off jujubes" or B) "Families gathered to shake jujubes"? A jujube is a fruit that is sometimes referred to as "a Chinese date." Of course, translation A makes more sense than B. In other words, the families gathered together to shake or strike jujube trees to cause the jujubes to fall to the ground, after which they could more easily gather them.

According to THIS KOREAN ARTICLE, 털다 means "to shake," and 떨다 means "to shake off," so you would "shake a jujube tree (대추나무를 털다) in order to "shake off jujubes" (대추를 떨다). Likewise, you would "shake your clothes" (옷을 털다) in order to "shake off the dust on the clothes" (옷에 묻은 먼지를 떨다). In other words, if the object of the sentence is the thing that is being shook, you use 털다, but if the object is the thing that is being shook off, you use 떨다.

The word 은행 can mean either "bank" or "ginkgo nut." 은행를 떨다 translates as "shake off ginkgo nuts," but the idiom 은행를 털다, which literally means "to shake a bank," translates as "to rob a bank." In other words, you shake the bank in order to get the money in the bank to fall out of it, as you would do with a piggy bank.