てある
te-aru
てある still has a person's fingerprints on it
The picture Something a person did deliberately and then stepped away from. Their intention is still sitting there. ている says it simply is that way; てある says someone made it that way and stepped back.
Where the picture shows up in てある
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stuck up and left there
ドアに紙が貼ってあります。
doa ni kami ga hatte arimasu
There's a notice on the door.
A sheet of paper hangs squarely on the door; whoever taped it there has already walked off.
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done ahead, ready and waiting
ホテルはもう予約してあります。
hoteru wa mō yoyaku shite arimasu
The hotel is already booked.
A confirmation email has arrived, and a hotel room sits empty, held under our name.
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chilled on purpose
冷蔵庫にビールが冷やしてある。
reizōko ni bīru ga hiyashite aru
There's beer chilling in the fridge.
Open the fridge and the beers are standing in the front row, turned so you can reach them.
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written down and still there
名前はここに書いてあります。
namae wa koko ni kaite arimasu
Your name is written here.
The name field on the form already has writing in it, and the pen is lying beside it.
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left open on purpose
窓が開けてあります。
mado ga akete arimasu
The window has been left open.
A window someone pushed wide for the breeze, its latch fixed in the open position.
窓が開いています just describes an open window; 窓が開けてあります says someone opened it and left it.
All of it in one picture
てある does not just report the state in front of you; it keeps the fingerprints of the person who put it there. The paper on the door, the room held under your name, the beers set at the front of the shelf, the name already written, the window fixed open — every one of them is a place where a hand touched and then withdrew. So てある never reads as 'it happens to be so' but as 'someone left it so'. The person has stepped out of frame; the intention is still inside it.