Yet and still can have a similar meaning, but this depends on the verb tense used and if it is affirmative, negative or interrogative.
YET is an adverb that we usually use at the end of a sentence. It normally means something that is expected to happen or something that is still in progress: When we use the interrogative form YET generally means the same as already: Have you finished the washing up yet? Have you figured out the answer yet? When we use the negative form YET has a very similar meaning to still (in progress) or hasn´t begun: I haven´t done the housework yet.
STILL is an adverb that generally means ¨in progress¨: We use STILL in the affirmative form in the present continuous: I am still listening to the radio, don´t turn it off! Also, we use STILL in the negative form with the present perfect, this way it means YET: I still haven´t met you parents and you still haven´t come to the UK to meet mine.
Fixed expressions with YET:
Yet still = even so, however
As yet = so far, up to now
So near yet so far = very close, nearly
Not just yet = not at the moment
Fixed expressions with STILL:
Still and all = nevertheless
The best is still to come = the future holds something better
It is still early days = it is too soon to call
Hold still = not move
Still going strong = continue being successful or healthy
The still of the night = the silence and calm at night
Yet and still can be confusing adverbs and you need to make sure you review them. Take a look at our posts on grammar structures (HERE) to get our free PDFs and practice and for more vocabulary take a look at our post on word patterns and collocations (HERE)