Wiggle vs. jiggle

Question

Whenever I have to describe a shaky movement I find it really hard to pick the right word. More specifically, I never know whether to use wiggle or jiggle. Dictionaries don't help much:

• jiggle UK /ˈdʒɪɡ.əl/ US /ˈdʒɪɡ.əl/
  to ​move from ​side to ​side or up and down with ​quick ​short ​movements, or to make something do this: If the ​door won't ​open, ​try jiggling the ​key in the ​lock.

• wiggle UK /ˈwɪɡ.əl/ US /ˈwɪɡ.əl/ informal
  to (​cause to) ​move up and down and/or from ​side to ​side with ​small, ​quick ​movements: He ​tried wiggling the ​control ​stick but nothing ​happened. She wiggled her ​toes in the ​water. Her ​hips wiggle as she ​walks.

[dictionary.cambridge.org]

From Google NGrams I see some common collocations for both verbs are jiggle cage, jiggle bars, wiggle room and wiggle eyes¹. Also, it seems that for body parts such as fingers, toes, or tails², wiggle is more common than jiggle. Actually, Google Ngrams doesn't return a single instance for "jiggle" with the aforementioned body parts.

If we move on to consider dance moves such as twerking, both verbs come up pretty often. As an example, take Jason Derulo's song Wiggle, or this video where a fitness instructor says "let the booty jiggle".

So, is there any difference in usage between "jiggle" and "wiggle"? When should I use each? Are there any instances where only one is correct or natural-sounding and the other is not?

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^{1: Some alternative expressions are wiggly eyes or googly eyes.
2: Even though wag is far more common to describe the movement of a tail, it seems wiggle isn't unheard of.}

Answer 1

Jiggle is a certain movement which is caused by an external force which causes a random or pseudo-random movement. Imagine a car driving on a bumpy road, things that might jiggle in the car are

jello on a plate jiggles
the surface of a cup of coffee jiggles
a woman's breasts jiggle ( not initiated by the woman, see below )

When things jiggle they usually remain attached.

Wiggle means not in a straight line. If something has a wiggle in it, it means it curves back and forth (not to be confused with "meandering"). Wiggle can also mean a certain non-straight motion within in a small space, sometimes to create more space.

Wiggling is usually caused by the thing that wiggles.

worms wiggle
paths wiggle, The Wiggle
wiggle wire
a woman's toes wiggle ( initiated by the woman )

When wanting to have less constraints or rules, one can ask for

more wiggle room

Also, The Wiggles are an Australian music group.

Answer 2

Peter got most of the way there, but I feel that suggesting the word used should depend on the thing causing the movement is wrong.

The difference between "wiggle" and "jiggle" is the control had in the movement.

If something jiggles it is uncontrolled... how far it moves, which direction etc etc may be constrained, but are essentially random.

If something wiggles then the movement is controlled.

An example where both words could be used reasonably. If someone were to say they jiggled the key in the lock, they're just moving the key around, probably annoyed that it won't open... they're just shaking it around there not caring how it moves. If someone said they wiggled the key in the lock, they're doing it to try and feel the pins move and are moving it more slowly and carefully.

Hence why, in the case where it SEEMS like it's the object that's doing the movement it's a wiggle, and when it's something having it done to it, it's a jiggle.