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Well, there has to be a stop of exhalation, because the "k" sound is a stop and that is basically the definition of a stop! One thing I want to be pedantic about though: this is not a glottal stop, which is a specific sound made by closing the glottis. "k" denotes a velar stop, which is different.
You can see this stop as a dark area on the spectrogram:
But here's the spectrogram of someone saying sky:
You can see there is the same dark area! Pronouncing a "k" requires cutting off the airstream in the middle of a word also. The duration is about the same; 30 or 40ms in both cases.
If you look further through "aus Kindern werden Leute" in an audio editor you won't see this dark area between "Kindern" and "werden", nor between "werden" and "Leute". These don't have stops between them, so the sound is continuous, even though they're separate words.
It's easy to see the stop in "Leute" - this is almost as complete as that between "aus" and "Kindern". Less obvious are those in "Kindern" and "werden" (both for a letter "d"), but you can also see the dark areas.
I hope this is enough to explain how what you're hearing between some words also occurs within words, and between many words this phenomenon doesn't happen. Phonetics is tricky. It's like learning to draw - at first you don't hear (or see) just what is there, but instead what you know is there. You know that "aus Kindern" or "das Kind" is two separate words, so you hear a break. You know that "Leute" or "sky" is one word, so you don't hear any break.
I've corrected my previous comments w.r.t. the terminology, thank you.
That being said, assuming those two spectrograms are using a comparable frequency scale, they show quite a bit of a difference: The upper spectrogram shows a near complete "black" stop across all but the lowest frequencies, while the lower spectrogram does not: The 2nd-lowest frequencies continue virtually unchanged, the mid frequencies are only reduced to a dark purple, not completely dark, and only the upper frequencies are truly dark. Those are not the same sound.
Well you're right that there is colour in the "sky" spectrogram, but if you loop the dark segment (easy in audacity) you will hear that it's just background noise. The "Kindern" sample has had noise removed or been recorded in a studio setting. It's also worth bearing in mind the colours are on a log scale; if you switch over to looking at the waveform you can see just how little is going on in both of those little gaps.
If this interests you there's a whole world of phonology and linguistics out there waiting for you... my mind was blown as a teenager when I learned about ich-Laut and ach-Laut.