Although inertial observers disagree about spatial and temporal separations separately, they agree on the spacetime interval between two events.

For one spatial dimension,

$$\Delta s^2=c^2\Delta t^2-\Delta x^2.$$

The same quantity is obtained after a Lorentz transformation:

$$\Delta s'^2=\Delta s^2.$$

Timelike, lightlike and spacelike separation

If $\Delta s^2>0$, the separation is timelike and one event can be reached from the other by an object moving slower than light.

If $\Delta s^2=0$, it is lightlike.

If $\Delta s^2<0$, it is spacelike and no slower-than-light causal signal can connect the events.

Proper time

Along a timelike worldline, the elapsed proper time is the time measured by a clock travelling with the object. For uniform motion,

$$c^2\Delta\tau^2=c^2\Delta t^2-\Delta x^2,$$

so

$$\Delta\tau=\Delta t\sqrt{1-v^2/c^2}=\frac{\Delta t}{\gamma}.$$

Proper time provides an invariant way to compare elapsed time along different spacetime paths. This is more precise than describing objects as literally having a fixed Euclidean 'speed through spacetime'.