Distinguishing articles in American English speech (with working audio)

Hi everyone!

I sometimes find it difficult to distinguish articles in American English speech. I even suspect they indeed sometimes pronounced identically. I'm not 100% sure though.

I'm listening to an audio book currently and I often hear 'a' where I understand it's 'the' even if I listen to the fragment like 50 times in a row (literally) in a kind of deep concentration trance.

I've made some clips. Could you please listen and tell me if the 'the'-s are pronounced differently from 'a' and what exactly the difference is? What are exactly the sounds?

The narrator is Scott Brick. He's from California.

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https://drive.google.com/file/d/1MqBKmLow6MjNpmuZ1NoTpOcqP3mJ-VkE/view

There was reason to the fact that the element known as “pure science” was
the freest form of life https://drive.google.com/file/d/1gnaKJPXKsX-zh2k44BYGMQ4zxJfz2KEv/view.

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https://drive.google.com/open?id=16fj_ZHYAFMKm7y2DHUvsbQ8mFsmRQPZi

So it also happened, that when Ebling Mis decided to allow Indbur to
honor him with an audience, he did not wait for the usual rigid line of
command to pass his request up https://drive.google.com/file/d/1591JMWPlqKNns3bhuZv7_ZPTOT5woolp/view, ...

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https://drive.google.com/file/d/1Lm8G-aR0yTniLpl0Dhhmg-1EbR0nqgKM/view

https://drive.google.com/open?id=1Ly4yPsknsr9rqmABPDCcSZRCThx105Xv with displeasure, and said haughtily https://drive.google.com/open?id=1-K16MGe16NoMc-A4RsSaFdkIDrMqfRPe
https://drive.google.com/open?id=1-K16MGe16NoMc-A4RsSaFdkIDrMqfRPe, ...