ASTC is just a detail. A texture compression is still being used even with a different name. I have asked you which one and you didn't respond?
There is a range of compression used - textures are often stored using DXT (based off of S3TC IIRC) which is largely lossless though there are some lossy variants IIRC but they are mostly not used. That is usually implemented at an application level though rather than driver so the application developer has control over the level of compression used.
ASTC (and the other forms) is not used in a context relevant to what you are talking about really - though it can be forced/recompression on texture upload which in some variants does result in a loss of detail that is generally not used on desktop hardware or forced at the driver level and mostly used on low end mobile hardware, etc. to compensate for very low spec. Even if it was in use and causing loss of quality it wouldn't manifest in the way you are talking about colour/quality differences - you'd largely just see banding on certain surfaces.
Internally delta compression (which at a simple level only transmits changes) and run length encoding is used in some parts of the GPU when transferring data especially colour information however these are lossless systems that have no impact on the fidelity of the data and typically result in between 1:4 and 1:8 compression of data.