全然ちがう話になるんだけどの英語

That is quite another thing [another kettle of fish].

That's another question―beside the question―aside from the subject.

〈約束と違う〉 That was not how I [we] understood it.

That's another story.

That's quite another thing to what you promised.

That's another question [story].

That's another story.

That alters the case.

That's quite another thing.

In that case, I'll change my mind.

That's not what you said before.

That's quite another thing―quite another pair of shoes.

The accounts are at variance with one another―not at one with one another.

What you say, is at variance with what others say

There is definitely something wrong.

But that is another story.

〈事実ではない〉 That isn't true [so] at all.

Talking is one thing, doing is another.

I is not so.

She tells a very different story.

That's another thing

It's emphatically not true.

They are (as) like as chalk and cheese.

This and that are two different stories.

That story and this story are different.

especially not

It's not true.

I take a different view of the matter

to be disappointed of one's expectations―reckon without one's host

That is completely different.