I think it's a good idea to get a glance at history. when we refer to Korean things we use the word "韓" because "韓" is an nation which existed in our ancient history, but when it comes to "漢(汉 as simplified chinese)", it's referring to "漢(Han Dynasty)" in China. we call ourselves "한민족(韓民族)", whereas the majority of chinese is called "한족(漢族,汉族 as simplified chinese)". actually 92% of Chinese is comprised of "漢族(汉族)" and the rest of them is the minor in China. unfortunately both are pronounced as "한(han)" in Korean.

It is like the difference between 漢 and this 韓.

'바보입니다' reminds me of Patrice Evar's comment '나는 바보입니다' copying what Park Jisung said without knowing what that meant. :-) 漢 is usually used for saying something related to China/Chinese characters like 한시(漢詩 poetry written in Chinese characters), 한문(漢文-writing/passage written in 한자漢字), 한자(漢字-letters/word). 韓 is mostly connected with Korea, such as 한국(韓國-Korea), 한복(韓服-Korean traditional clothing), 한옥(韓屋-traditional Korean style house), etc. However, every word isn't in accordance with this pattern. For example, 한양(漢陽) was the name of a capital city of Chosun dynasty, which refers to Seoul today. The Han river in Seoul is also written as 한강(漢江). 악한(惡漢-evil man) is one of many I should try to figure out why that Chinese character is used. Many people don't care which 한자 is used for the words. But it can't be deniable that knowing 한자 helps improve your comprehension. So, way to go! :-)