It seems to me that all songbirds make begging calls, either when they are hungry chicks in the nest, juvenile fledglings angling for a handout from mum and day, or as adults communicating their submission during fighting or mating.
The most sure-fire way to learn the begging call of a species is to locate a nest (often easier said than done) and listen for the sound young birds make when a parent is incoming with food. The hungry chicks will make begging calls of a remarkably vociferous and urgent nature while the parent is at or near the nest. Once the parent leaves to forage for another tidbit however, the chicks quiet down immediately (which is advisable if they are hoping not to sound like an advert jingle for fast food snacks).
Because begging calls are indicative of young and not-yet-fully-independent birds (ie. incautious, incapacitated and defenceless birds), predators go around the place listening with great interest to calls of this nature. Birds rarely develop to independence in the nest, instead opting to leave the confines of their birthplace as soon as their legs and / or wings allow them. This is because nests act as a sensory mecca for attracting nosey predators. It is safer to get the heck out of Dodge, even if that means being fed while awkwardly clambering around the foliage or ground for a few weeks.
Whilst most small songbirds become independent from their parents after a couple of weeks in the big wild world, larger (and typically longer-lived) species such as cockatoos, can be heard using their juvenile food-begging voice for up to a year or more after leaving the nest. If you’ve ever had a juvenile Yellow-tailed Black-cockatoo anywhere near your house, you’ll have some sense for just how incredibly annoying their incessant begging can be. Actually, juvenile magpies aren’t much better.
Incidentally, in the case of my children, their begging voice (a persistent whinging sound) was still going strong after 16 years!

Begging-type calls can also be made by adult birds during expressions of submission. Deployed together with a set of distinct body posturing adult birds are able to signal they’ve had enough during a heated dispute. Similarly, almost the exact same voice and physical gesture combo are often seen when a female bird is confirming to her partner that she is ready to get down and dirty (yeah…I’m talking about sex).

In most songbirds where I have observed submission, the calls appear so similar to chick begging calls (especially older chicks and fledglings rather than the high-pitched squeaking made by very young chicks) that I lump them both under the same voice category.
The rapid flickering of lowered wing tips, open-gaped bill, supine head posture and arched body adopted by adult birds engaged in submission gestures (either to end disputes or to indicate sexual readiness) perfectly resemble a hungry chick begging to be fed.
And in this video you can clearly hear how songbirds need to learn control over their vocal systems, rather than it just being an inherited instinct from birth (like with non-songbirds). It took months of practice for this young Laughing Kookaburra to start making proper rollicking kookaburra calls.
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