elanvital Both of your sentences can be used to talk about the same event. What is the difference? Here is a simplified explanation. They hanged the wrong guy. (at a moment in the past--the time is usually mentioned) It happened in the past. The past simple is used when there is an exact time mentioned. If the time is not mentioned, as is the case here, the speaker has the past moment in mind; in American usage it may refer to the recent past, perhaps one minute before. The listener knows it is relevant now only by context, that is, only because the speaker is mentioning it now. They have hanged (or hung) the wrong guy. (no time mentioned) It happened-- and is relevant now. The exact time when it happened is not mentioned in the present perfect. The use of the present tense verb "to have" brings the event into the present and makes it important now for the speaker and listener. This is done because it happened in the recent past (British usage) or because the past event has importance for the present moment in the mind of the speaker.

There is no difference in meaning.

Thanks everyone for your help!

if you really want to empasize it you could use a southern accent and say "well tarnation, they done gone and hanged the wrong guy!" hanged/hung: （彼らは）違う男を絞首刑にした。 have hanged/have hung: （彼らは）違う男を絞首刑にしたことある。 現在完了は二つの言語で同じ意味だけど、英語でと日本語でと気持ちが違うと思います、そして使う理由も違います。英語で、現在の関わりを強調するの為に使う、でも日本語であの文”違う男を絞首刑にしたことある”どう思われますか？へんですか？悪い事を和らぐの為に使ってるでしょ？

The first sentence emphasizes the action in the past. It simply described what happened in the past. The second sentence emphasize the current influence or result of a past action. That is the guy is dead.