A digital recording takes snapshots of the analog signal at a certain rate (for CDs it is 44,100 times per second) and measures each snapshot with a certain accuracy ... This means that, by definition, a digital recording is not capturing the complete sound wave. It is approximating it with a series of steps. Some sounds that have very quick transitions, such as a drum beat or a trumpet's tone, will be distorted because they change too quickly for the sample rate.
While this seems intuitively true, it is actually completely false, demonstrably so. See this.
A vinyl record has a groove carved into it that mirrors the original sound's waveform. This means that no information is lost.But information is lost. That's easy to prove. Ask anyone who has ever made their own recording and then had an LP pressed from it.
Not to nitpick, but a groove is not "carved" into an LP. It is stamped. Only the master lacquer can be considered to be "carved."
I'm a vinyl guy, so I hesitate to correct these errors. But it's important to understand what LP gets right, and where it has limitations.

