We all move at the same speed

When you speed up through space, time slows down relative to someone who remains still. If you are standing still in a particular frame of reference, almost all your motion through spacetime is through time. But as your speed through space increases, your passage through time decreases to keep the overall spacetime relationship balanced.

In that sense, we are all moving through spacetime, but in different proportions. The faster you move through space, the less you move through time relative to someone at rest.

A useful analogy is travelling north-east. If you travel due north, your easterly motion is zero. If you travel due east, your northerly motion is zero. If you travel diagonally north-east, your movement is shared between both directions. Spacetime works in a similar way: motion can be divided between space and time. The more of your motion that goes into space, the less goes into time.

So, in a simplified sense, we are all moving through spacetime at the same underlying rate, but with different proportions of motion through space and motion through time.