The atmosphere had relaxed a bit. Still/Yet, I couldn't stop thinking how strange it was to watch my brother being insecure.
Which on is the correct choice? I often get confused about which one to use. They seem interchangeable to me most of the time.
From Subscrioption-Only LDOCE:
Yet is used to say that something has not happened or a situation has not started to exist, or to ask if something has happened:
It isn't time to go yet.
Have you seen him yet?
**Still* is used to say that an earlier situation has not changed:
This system of naming is still used today (NOT yet used today).
I still don't understand.
So I'd say in that sentence it's better to use still, rather than yet, because you had been thinking, and it hasn't changed so far, and you are still thinking.
They are technically interchangeable, but yet is a little more old-fashioned and formal. Given the tone of your sentence, I would use still.
Also, it should be relaxed, not relax, and see would be more appropriate than watch.
Both yet and still are adversatives, i.e., words used to indicate or acknowledge a kind of dialectical tension between sentences or clauses, as representing two more or less opposing viewpoints. This category also includes but, however, [al]though, nonetheless, and nevertheless. Many of these words have other functions and senses as well, notably including yet and still, but I believe this question deals with their shared adversative sense.
In this sense, yet functions as a coordinating conjunction, still as a conjunctive adverb.
Because of that difference, they are punctuated a little differently. In the case where a period precedes the word (so that sentences are being contrasted), still takes a following comma more often and comfortably than yet does (though you can go either way with either). Thus—
If a period does not precede, yet works fine with just a comma or nothing at all before it (and nothing after it, either), while still is happier with a semicolon before and a comma after.
