They are nouns that mean “in the middle of”. They are used to express situations in which an action/event has begun and has not finished yet. They are mostly interchangeable but the nuance is a little different.
“途中” just indicates the certain point of the action/event. When you want to say “on the way to somewhere”, you have to use “途中”.
“最中” indicates the most active point of the action/event.
Ken and Leo work at the same office. Leo is with his subordinate in a meeting, but Ken is trying to talk to Leo because something has come up.
- Ken: I'm sorry to interrupt you but it’s a phone call from your client. He is calling to inquire of the project cost. He is in a hurry because the deadline for submission of the estimate is approaching.
会議の途中(or最中)で申し訳ないけど、お客様から電話が入っている。プロジェクト費用についての問い合わせだよ。見積もりの締め切りが近づいているから、急いでいるみたい。
→ In this case, he can use “途中” and “最中”. If Leo is in the middle of an important meeting, “最中” is better to use. - Leo: Okay. I'm in the middle of a meeting so can you tell him that I’ll call him back in 10 minutes?
わかった。会議の最中だから、10分後に折り返し電話する(*1)って、伝えてくれる?
→ In this case, he wants to emphasize that he is busy at the meeting right now. That’s why “最中” is better to use - Ken: All right.
了解。
Ken is asking Leo about his impression of the movie that Ken recommended.
- Ken : How did you like the movie?
映画はどうだった? - Leo : I’ve only watched a part of it. I liked it so far.
途中まで見たよ。面白いね。
→ In this case, he just wants to explain how far he has watched. That’s why “途中” is used. - Ken : Nice to hear.
よかった。 - Leo : I wanted to watch the whole movie, but the construction in my neighbourhood started while I was watching it. It was too noisy.
全部見たかったんだけど、見ている最中に、近所で工事が始まったんだ。うるさくてさ。
→ In this case, he wants to explain the moment that he focused on watching the movie. That’s why “最中” is better to use.
Meg is at home. She is calling her sister to get some snacks.
- Meg : I’m going to watch a TV drama tonight. Could you stop by a convenience store and get some snacks on your way back?
今夜ドラマ見るの。家に帰る途中、コンビニでお菓子を買って来てくれない?
→ In this case, she wants to say “on one’s way”. That’s why “途中” is used. - Her sister : Okay. I read the original book that the TV drama is based on. That story gets more interesting partway through.
いいよ。あのドラマの原作(*2)本読んだよ。途中から面白くなるよ。
→ In this case, she just wants to explain the certain point of the story. That’s why “途中” is used. - Meg ：No spoilers!
ネタバレ(*3)、やめて！
*1 折り返し電話する: It means to call somebody back.
*2 原作: It means "the original work of something".
*3 ネタバレ: It means to spoil a story.