I recently came across the kanji 燕, and found out about 嚥 today.
According to jisho.org, both translate to "swallow", except that the first one means swallow bird and the second one (with the "mouth" radical) means the act of swallowing.
Both kanji look very similar, and both English words are homonyms. After some research, I found that some people pointed out the fact swallows swallow insects and hold them in their throat to feed their youngs, which indicates this pair of words could be related at the other end of the world too.
It still seems mysteriously coincidental to me, which is why I decided to ask.