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: 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 : 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 : 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.