What exactly does this joke mean?

It should refer to a story: a farmer met an alien, the alien held out three fingers, the farmer held out five fingers, the alien made an "eight" gesture with his thumb and forefinger, and the farmer held out his thumb.

When the farmer came home, he said to his wife, "I met a clever alien today." He said he wanted three cucumbers. I said I'd give him five more cucumbers. He said there were eight cucumbers. I gave him a thumbs up. "

After returning to space, the alien said to other aliens, "I met a powerful earthman today." I said I killed three pigs today. He said he killed five people. I said I shot him with a gun. He said he killed him with his thumb. "

This story shows that language barriers usually lead to misunderstandings.