die Klinke
door handle
A usually L-shaped handle on a door that you press down to open the door.
Er drückte die Klinke herunter und trat leise ins Zimmer.
He pressed down the door handle and quietly entered the room.

handle / jack
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door handle
A usually L-shaped handle on a door that you press down to open the door.
Er drückte die Klinke herunter und trat leise ins Zimmer.
He pressed down the door handle and quietly entered the room.

For a door, 'Klinke' (door handle) is almost always used with the verb 'drücken' (to press) or 'herunterdrücken' (to press down). This describes the typical hand movement used to open a door.
Bitte drück die Klinke leise herunter, das Baby schläft.
Please press the door handle down quietly; the baby is sleeping.
The idiom 'sich die Klinke in die Hand geben' (to come and go in large numbers) is a fixed unit. The verb is reflexive ('sich'), and the subject is in the plural because it is always about several people coming and going.
Vor Weihnachten geben sich die Kunden im Kaufhaus die Klinke in die Hand.
Before Christmas, customers are coming and going at the department store.
You can tell from the context whether the door handle or the plug is meant. Words like 'Kopfhörer' (headphones), 'Kabel' (cable), 'Anschluss' (connection/port), or measurements like '3,5 mm' clearly point to the audio plug.
Der Stecker passt nicht, ich brauche eine kleinere Klinke für mein Handy.
The plug doesn't fit; I need a smaller jack for my phone.
handle / grip
'der Griff' and 'die Klinke' can both refer to something you take hold of with your hand. 'Griff' is general and can be found on many objects. 'Klinke' is much more specific: it is the door handle that you usually press down to open a door. Learners may confuse the words because a 'Türklinke' is indeed a kind of 'Griff'. If it is not about a door, 'Griff' is usually the right choice. For a normal door, 'Klinke' is more precise.

Du musst die Klinke vorsichtig drücken, sonst macht die Tür Lärm.
You have to press the door handle carefully, otherwise the door makes noise.
Der Griff am Koffer war locker, aber er hielt noch.
The handle on the suitcase was loose, but it still held.