they are totally the same thing. in fact, 喝醉 is more official. that's all

喝醉just means you are drunk,it is used more usually and formally.喝高means you are drunk and you drunk too much.sometimes you will feel uncomfortable or have a headache.It's spoken language.

我未曾聽聞台灣人使用 "喝高" 一詞 但依我的理解 "喝高" 應該不等於 "喝醉" "高" 並無 "醉" 的解釋 "高" 應該是 "超越一般的水準" 之意 "喝高" 即 台灣人常用的 "喝多了"

I guess 喝醉 is like drunk in english and 喝高 is like tipsy

喝醉 refers to intoxication , befuddle, For example, 你已经喝醉了,走路遥遥晃晃的 喝高 refers to you have drink too much ,but it does not mean you are drunk. 你已经喝高了,就不要再喝了.