There's some nuance in your original two sentences, beyond a present/past setting. It's also a little different, or difficult, because it sounds like it's legal language, which is quite specific and unique in how it's used. You need to have an understanding of that language in order to correctly interpret it. I don't!
I'm wondering about the smaller words in each of the sentences you've shared - these are what change the meaning, to me. The first sentence has 'on' - it would make more sense to me if it used 'for' or 'from'. So I wonder what the specific use and meaning of that word in this sentence is. I'd agree with David that it's not about fact, but that these two variations differ in meaning in some other way.
Your last paragraph - The date of unit redemption appeared in your bank statement was 1 January 2020 which differed from the date shown in the David Trust unit register being 15 January 2020. Thanks! - also makes me wonder about the preposition used: 'of' doesn't seem to fit here. Is it correctly copied, or is the 'of' perhaps meant to be 'the', or something similar? If it's correct, then that means 'was' is out of place. I would normally think 'of', 'for', or 'on' should go there. There should also be some commas, which would make it clearer (before 'being' and 'which'). Perhaps the writer made a mistake with one of those words (the commas aren't a big deal, but do help - and if they've been omitted, then it makes me think there could also be mistakes with words). Context would help here.