There is one case where "still" and "yet" can have a similar meaning in English. That is when they are used to show contrast in a sentence. They can both have a meaning like "sin embargo" or "no obstante"
He is very tired, and yet he keeps working
He is very tired, but still he keeps working.
I love heavy metal; still, I don't like going to heavy metal concerts.
I love Heavy Metal; and yet, I don't like going to heavy metal concerts.