閉める, 締める, 閉まる, and 締まる: closing or tightening
Separate 閉 for closing a door or shop from 締 for tightening a cord, belt, or screw. See how the object and resulting state distinguish words pronounced しめる or しまる.
閉める and 閉まる for closing an opening
閉める is used to close an open place such as a door or window. 出かける前に窓を閉めてください。 marks the window being closed with を.
閉まる describes a door or shop becoming closed. この店は午後六時に閉まります。 says that the shop closes at six p.m., with 店 presented as the topic by は.
締める and 締まる for making something tight
締める is used to tighten a cord, belt, or screw. 自転車に乗る前に、ヘルメットのあごひもを締めます。 marks the chin strap being tightened with を.
締まる describes something becoming tight or secure. このねじはまだ十分に締まっていません。 says that the screw is not yet sufficiently tightened.
Look at the object and meaning before the sound
Write ドアをしめる as 閉める because a passage is being closed, and ベルトをしめる as 締める because something loose is being tightened. The pronunciation alone cannot select the spelling, so check the object first.
締める can also mean bringing something to a close. 司会者が短い挨拶で会を締めました。 says that the host concluded the event with brief closing remarks. Do not confuse this figurative use with 閉める for doors or windows.
Quick check: Which characters are used for しめる when closing the front door and when tightening loose shoelaces?
Show the answer and why
Write 玄関のドアを閉める for the door and 靴ひもを締める for the laces. Use 閉 to close an opening and 締 to tighten something loose.