Is an APS-C lens labeled with an effective or true focal length?

I know that the effective focal length of the 50 mm FX lens is actually 50 x 1.5 = 75 mm, because I am shooting with an APS-C sensor.

Not quite. It is not "wrong", but you have to understand what it means. The 75mm will not be a useful number in DX. The 50mm lens is NOT 75mm, and there is no real thing called effective focal length. It is a purely hypothetical concept. Any lens (at any zoom) only has a focal length, where it actually focuses light from infinity.

The 50mm lens is always only 50mm, regardless of whether it is on a DX or FX sensor. It's 50mm, period. That's why it's marked 50mm. 50mm is the only focal distance it has.

Now you may want to compare your field of vision with some other lens in some other sensor. And it is true that the smaller size of the DX sensor reduces its field of vision, so (if it is with a 50mm lens) its reduced field of vision is compared to what a 75mm lens would look like in a frame. 35mm film (or an FX frame is the same size as a 35mm film). But if your lens has a 50mm mark, the 50mm lens always remains on any sensor.

The effective focal length is only on the other lens on that other sensor (35mm film), just because the other 75mm lens seems to have the same field of view in the 35mm film (or FX is the same size) as the 50mm lens in the DX sensor. The focal length in the DX sensor is 50 mm. Only the other lens is 75 mm, and if it is in that other larger sensor, it has the same field of vision as the 50 mm in DX. We are talking about two different lenses and two different sensors.

The point of this is that there are many people who used 35mm films for years or decades. They are very used to what a 50 or 75 mm lens will see and do exactly in a 35mm film. Your experience simply knows it.

The smallest digital sensors of today change things (narrow field of view of the smallest sensors). This smaller sensor now requires shorter lenses, to see the "same width of view" that the larger 35mm film always saw. So your experience no longer only knows (yet) in your new camera. So the point of this "effective focal distance" thing is to compare, to tell users familiar with the 35mm film what a certain lens will do with its new sensor cut out. If we say that this 50mm lens works in DX like we are used to 75mm in 35mm film (field of vision), then this has meaning for them, they know what to expect from it. However, if you are not familiar with the use of a 35mm film, the effective focal length on a 35mm film is probably not a useful concept for you.

The effective focal length published with lenses for smaller sensors. forever it is compared to the 35mm film size (which is equal to the size of FX, called the full frame). However, we can compare the field of view of two sensor sizes. For example, imagine 1/2 inch and 2 inch sensors (film maybe). The largest is 4x larger than the smallest, so the clipping factor is 4x, and (with the same lens) the larger one will have a field of view 4x wider than the smallest, and you will need a focal length effective 4 times more to see The same field of vision reduced than the smallest. Different sensors can be of different shapes (3: 2, 4: 3, 16: 9), so the clipping factor compares the diagonal of the frames.

For FX and DX, this ratio is 1.5x.

A similar proportion was always valid for different film sizes, but not until FX and digital DX were able to use the same lens in different sized sensors. So this becomes a topic of discussion today.