As you know, yet and still can be adverbs of time.
- Mike is still at work. He hasn't repaired the sink yet.
However, as conjunctions, yet and still appear at the beginning of clauses and have different meanings:
still means something similar to "nevertheless, admitting that".
While yet means "inspite of that/all the same/nevertheless"
- Mike is not hard-working; still, he has managed to become a millinaire.
- The films is boring; yet people go to cinema to watch it.