Not necessarily. On a macro scale for general human interactions, for the most part, but the only thing observers have to agree on is space time interval and causality. Space, time, and order (if not important to causality) might be different.

In the presentation of SR I saw, "observers" are basically identical with reference frames. What is "observed" is exactly the sequence of events pieced together from instruments in that reference frame, close enough to "see" all the relevant events with negligible lightspeed delay, all with synchronized clocks. "Seeing" a distant event, the time when light from that event reaches a particular point, is an entirely different question that, frankly, we mostly ignored.