So I watched 古装 TV drama, I heard these sentences quite a bit. But not quite sure the 终 or the 总 they were using. Which ones are correct?
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终有 --> 终於有 (will finally be)
总有 --> 总会有 (will always be)
终有 stress 'eventuality'
总有 stress 'inevitability' and 'certainty'
Both 终有一天 and 总有一天 can be translated as 'there will be a day'
人总有失望之時 -- All people will inevitably have disappointment
人終有一死 -- All people will eventually die
大家一起想辨法，总能解決問題的 -- Let us all think together, we can certainly solve the problem
大家一起想辨法，終能解決問題的 -- Let us all think together, we'll be able to solve the problem at the end
All of them are correct. I partly agree with Tang Ho's answer, which 终 presents finally, and 总 presents always. But putting them into these sentences, their meanings are the same. 终将 is a more graceful expression when you are writhing Chinese, or doing a presentation. And when we speak Chinese, we usually use 总. So, when you are writing, 终有一天我会成功 is better. But since 报仇 is not graceful, it is better to say or writhe 总有一天我会报仇.