What's the origin of "-er" vs. "-re" endings?

There’s some words that end in "er" or "re" depending on the word, and depending on what country you learned English from.

There’s words like reader with the "er" ending, but that’s because reader is derivative of read, and the "er" is tacked on at the end to create a noun.

But there’s cases where creating a noun is not the case, and it’s not as clear why an ending was chosen. There’s center in American English, and centre in British English, which I always chalked up to weird spelling quirks between the two forms of English (similar to color vs. colour). The weird spelling quirk doesn’t explain why there’s words that aren’t derivative of other words like acre, mediocre, etc. which always use the "re" ending, or like river, letter, member, etc. which always use the "er" ending. They’re both examples of words that use these spellings regardless of your country of origin, but it’s not exactly clear why that is, or why there’s even a difference between British and American English spellings of words.

Why is this? Is there some etymology behind the "er" vs. "re" ending of words?