When compared with air particles in a silent room how are the particles in compressions and rarefactions different?

Obviously the particles themselves cannot be different.

Even when you go further all particles in the room are moving.
So if you take any one particle and study it you cannot know if it is a part of sound or not.

Sound is an aggregate of millions upon millions of particles.
If you took a slice of the air and found the velocity of each particle in that slice then averaged all of that. ( as a vector of course )

Then moved slightly and took another slice and found the velocities there then the average of the second slice would be the same as the average in the first slice in a silent room.

It would NOT be the same if there was a sound present. Different parts of the air would have different average velocities so some parts are moving towards each other and some parts are moving away from each other.

Get a dictionary and study the words.