As you have already mentioned, 그런데 means same as but and however, and also moving on to a new topic. 그런데 can be used in many ways. Moreover, I suppose you have also heard of 근데 which is a shorter form of 그런데. I know you are quite aware of the meaning of those words, so i will give you some examples. 나는 샤워했어, 그런데 너 어제 맥도날드 누구랑갔어? I just took a shower, by the way who did you go to Macdonald with? 나는 그남자 별로안좋아해, 그런데 너는 누가좋아? I am not that interested in that guy, in anway who do you like? This is a noticeable difference between 그런데 and 하지만. However, when you wanna say but or however in Korean, there is no significant difference between them. What you can also use is 그러나. 근데( 그런데) can be also used to mean "so what?" if you like watching korean dramas, im sure you've heard of it sometiems. Some examples : 근데 어쩌라고? so what, what do you want from me? I apologize if it makes you more confused :D hope you enjoy studying korean

그런데 is a little bit complicating. When you hear Korean people's talking, you can hear many times. That means '1. well, anyway, by the way / 2. but, however' First of all, when we want to change a topic, making connect with the topic before we talked about, we use '그런데' in the middle of two sentences. For example, 아 그렇구나, 그런데 왜 그때는 얘기를 안했어? I got it well, why didn't you tell me at that time? 아, 네가 철수구나. 그런데 네 나이가 어떻게 되지? Oh, you are 철수, by the way how old are you? Second of all, If you want to write contrast's sentences, you can put '그런데'. For example, 동생은 벌써 숙제를 다 했어요. 그런데 저는 아직 다 못했어요. My little sister has completed her homework already, but I haven't. 나도 파티에 참여하고 싶어, 그런데 나 지금 바빠서 가야 돼. I want to join the party with you guys, however, I have to go because I'm busy. Does it make sense? 도움이 되었으면 좋겠어요 :)