つく
tsuku
Stains stick, and so does confidence: つく
The picture Something landing on a surface and staying stuck to it. つく is what sticks on its own; つける is you sticking it.
Where the picture shows up in つく
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it gets stuck on
白いシャツにコーヒーのしみがつきました。
shiroi shatsu ni kōhī no shimi ga tsukimashita
I got a coffee stain on my white shirt.
A drop of coffee spreading and clinging to the chest of a white shirt
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your body sticks to the destination
あと十分で駅に着きます。
ato juppun de eki ni tsukimasu
We arrive at the station in ten minutes.
A body that was moving touching the platform and sticking there
Written 着く, but it's the same picture: you land on the spot and stay.
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the light is stuck on
部屋の電気がついています。
heya no denki ga tsuite imasu
The light in the room is on.
A bulb in the ceiling with the light caught on it and staying lit
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the skill sticks to you
日本語に自信がついてきました。
nihongo ni jishin ga tsuite kimashita
I'm starting to feel confident in Japanese.
Confidence sticking to you one layer at a time each time you speak Japanese
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it comes attached
このホテルは朝食がつきます。
kono hoteru wa chōshoku ga tsukimasu
This hotel includes breakfast.
A hotel room key that comes with a breakfast coupon attached to it
All of it in one picture
つく is the picture of something landing on a surface and staying stuck. A drop of coffee sticks to the shirt; a moving body touches the platform and sticks there; the light catches on the bulb and stays lit; confidence sticks to you a layer at a time; breakfast comes attached to the room key. Only what sticks changes — a stain, your own body, a light, a skill, a service. So a つく sentence carries the feeling that nobody arranged it: it just stuck.