Question: Do the two identical words in these two questions express the same meaning?

It's different, because the parts of speech are different.

Girls who don't tie their feet will be laughed at. Laugh

. Grandpa's jokes are not funny at all. Laugh

The first laugh is a verb, the second joke is a noun, and the funny one is an adverb

, which deeply hurts his young heart. Sting

? It stuck in his throat like a thorn. Thorn

The first thorn is a verb and the second is a noun.