The verb 살다 has an interesting connection to other words in the Korean vocabulary relating to living and burning.
- 살아나다 (to revive)
- 사르다 (to burn)
- 삶 (life)
- 사람 (person)
- 사랑 (love) (possibly related)
- 숨 (breath) (possibly related)
There was an academic paper I read a long (giving my age away here, hehe) time ago relating to the Korean view of human life that also suggested how the words are etymologically connected to dirt/the ground (흙). I cannot seem to find it anymore. Part of the process of connecting 흙 to 살 is highlighting the tendency of [s] to debuccalize to [h] in languages. In Korean, this would have been a historical sound change that happened long before it had a phonetic script.
Anyway, the argument of that particular paper was (paraphrased) that Koreans viewed humans as beings that arise from dirt, burn, and return to the ground completing their version of “the circle of life.”
Usually 살아요 will be a statement like I live there + 사세요 is a request, please live there. Maddeningly they can switch sometimes (like in the example given by LiKenun above) but most of the time ~세요 is the imperative ending of a verb.
살다 (to live) is a little unusual btw, because some of its conjugations are exactly the same as 사다 (to buy). More often you'll see 사세요 meaning please buy something. 99% of the time it will be obvious which one it is...