They may be homophones, but many are far too young to be mining for bismuth.

As others have pointed out, these words are homophonous in most North American English dialects, but for more context, this is due to a phenomenon called flapping.

Basically, even though /d/ and /t/ are phonemic (that is, contrastive; speakers can use them to distinguish words and hear them as different sounds) in English, in certain positions in the middle of a word (specifically when placed between a stressed vowel and an unstressed vowel), both the /d/ and the /t/ become a different sound, flap/tap. See, e.g. butter, bottle, writing, riding, wedding, loader, etc.

And, since they both become flap in this position, the contrast between them is neutralized, meaning that they are pronounced identically and speakers can no longer tell them apart, creating many sets of homophones in the process like "latter" and "ladder".

There are further interesting complexities in flapping across English dialects, in particular the interaction of flapping with Canadian Raising, so if anyone has any questions or wants me to go into more detail, let me know!

Found the Brit.

Latter and ladder are homophones in most of American english

In my dialect/accent, ladder and latter are full homophones when spoken.

Depends on the accent of course.

in American English they sound identical.

ladder

laddter

speaking them fluidly, one can't tell the difference.