The difference between yet and still

Yet and still are used to talk about things that have (or haven’t) happened over time. Their meanings and uses are distinct. However, there is a situation in which they are used in a similar way to convey a similar idea. This is why learners get confused. 

Let's look at the uses of these two words separately, and then look at how their uses converge.

YET

The word yet is mainly used to refer to something that a person is waiting for and expecting, but that hasn’t happened so far. It is most common in negative statements and questions: 

• Negative statement: It isn’t raining yet. (=Rain is expected, but it has not started.) 

• Negative statement: The research has not been completed yet. (=Research has started, and the speaker thinks or hopes it will be completed soon, but so far it has not been completed.)

• Question: Have the kids had dinner yet? (=It is expected that the kids will have dinner; the speaker is asking whether this has happened already or not.)

STILL

The word still is used mainly to refer to something that began in the past and is continuing into the present. It is most common in affirmative statements and questions:

• Affirmative statement: He still lives far away. (=He used to live far away, and he continues to live far away now.)

• Affirmative statement: It’s still snowing! (=It was snowing in the past, and it continues to snow now.)

• Question: Do you still want to come over for dinner? (=Earlier you said you wanted to come over for dinner. Is that also true now?)

YET and STILL

Both yet and still can be used in negative statements to talk about something that wasn’t true in the past and continues not to be true in the present. This is where yet and still converge. For example, the two sentences in each pair below, one with yet and one with still, mean nearly the same thing.

• She hasn’t arrived yet.  =  She still hasn’t arrived.
• The reasons haven’t become clear yet.  =  The reasons still haven’t become clear. 

Notice however that yet is usually placed at the end of the sentence¹, and still is placed before the verb. In addition, most English speakers would say that the sentences with still include a sense of impatience that the sentences with yet do not have.

I hope this helps.

¹Note for more advanced learners: Yet is sometimes placed before the main verb, as in, "I haven't yet received an update." This is less common and perceived as more formal.