One thing's got nothin' to do with the other
心猿意马并不好里昂你明白吗?Change ain't good, Leon. You know?

我知道Yeah.

检查一下Check it.

确定这玩意儿没问题Make sure it's the right thing.

我相信你I trust you.

相信别人容易出事One thing's got nothin' to do with the other.

你要记住里昂Remember that.

我会的I will.

what is"one thing and the other refer to" in here?

the dialogue begins with the 45 minutes and 17 seconds in LEON

Question

One thing's got nothin' to do with the other
心猿意马并不好 里昂 你明白吗?Change ain't good, Leon. You know?

我知道Yeah.

检查一下Check it.

确定这玩意儿没问题Make sure it's the right thing.

我相信你I trust you.

相信别人容易出事One thing's got nothin' to do with the other.

你要记住 里昂Remember that.

我会的I will.

what is"one thing and the other refer to" in here?

the dialogue begins with the 45 minutes and 17 seconds in LEON

Answer

It essentially means that thing1 is not related to thing2.
They are irrelevant to each other.

For example:
Person A: I speak english.
Person B: I love cooking.

English and cooking are not related.

So Person C could say: One thing has nothing to do with the other.

I hope this helps you out !