Hi,
This is a very common question and a source of confusion. I have written several articles on the topic but they are in spanish. In summary, focal lenght is a physical property of the lens. It is what it is regardless of digital or film, movie or still, new or old. What changes is how much of the image is recorded.
This drawing gives you an example:
(just for translation: LUZ = light, largo focal = focal lenght and lente=lens My name is the same in all languages

)
This lens is of a given focal lenght. As you can see, the image is creates is the same. What changes is how much of it is recorded.
When digital came into the scene, marketing used the "equivalences" referencing to film. Since an APS-C sensor records a smaller portion of the image, it has a similar field of view as if it were taken with a longer lens in a film camera. That's where these factors came from.
The perspective doesn't change. Just how much is recorded.
Usual APS-C is a 1.5x crop factor. Canon APS-C is 1.6x and micro 4/3 is 2x. Similarly, a bigger sensor like medium format would be less than 1X depending on the size. It is all just referenced to the standard 35mm because it was (and still is) the standard of the world.
Hope this helps.
Thanks,