[Question][Theory]Comparison of measurement of time in Classical and Special Relativistic Mechanics. Part 1.

I'm having some trouble understanding the construction of reference frames and measurement of time in above two topics. Here it goes:

In Classical Mechanics, an observer A constructs his/her frame by picking up a coordinate system (usually, a 3D Cartesian grid for our assumed 3D world) and a clock. The clock and observer are at rest w.r.t observer's frame. An event "e" is described by observer as happening at (x,y,z)eA and at time (t)eA. Another observer B could be, w.r.t A, moving with constant velocity/acceleration/rotating and so his/her frame. B measures an event "f" at (x,y,z)fB and (t)fB. Here we say that clocks in all frames are synchronized,i.e., reading same time at any instant.

Question: Observer A records event "e" happening at (x,y,z)eA & (t)eA; as A's clock reads (t)eA, B's clock also reads (t)eA (due to our absolute time assumption). But this is not sufficient to say that (t)eB (time at which event "e" occurs acc. to B) also equals what B's clock read at that time, i.e., (t)eA; at some (x,y,z)eB. I mean to say, just by saying that time is synchronized in all frames, we can't say an event which occurred at time t in one frame, also occurred at time t in another frame or can we?

Thank you.