In mechanics there is a relative concept of "inertial frame": frame A is inertial with respect to frame B if A moves uniformly with respect B. That concept is easy to understand.
There also seems to be an absolute concept of "inertial frame". I keep reading things like "A is an inertial frame", without specifying with respect to which other frame B. Every time I read that kind of statements I get stuck. I cannot see how A can be "inertial". I can only see how it can be "inertial with respect to B".
Related to this, I keep reading things like "the solar system is accelerating" or "an object is moving" (for example here and here). Those statements I simply can't understand, unless they specify with respect to what frame (or object) that movement is defined.
I suspect my inability to understand the absolute concept of inertial frame is related to my inability to understand the statement "an object is moving". I only keep wondering: "with respect to what?".
So, my question is: can you really say "A is inertial" or "B is moving" in an absolute sense? (i.e without adding "with respect to C"). If so, how is that interpreted?