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What is the difference between space and space-time in this scenario? Honest question, since you move in time with velocity in space
Spatial movement
Since the 4th dimension of space is just an infinite amount of 3rd dimensions of space stacked infinitely tight and which is tangent to the normal vectors of every other spatial dimension, you could flip or pass through it just fine. All people and objects you know would disappear and you'd be faced with a new and alien world where every physical object and phenomena is off. Unless, of course, if you not only witness translation, but also rotation, in which case you might be able to see parts of your own dimension from a fucked up point of view, aka. being able to see the organs inside people etc..
Obviously, this assumes that our 4D space is part of a 5D space-time such that at least 1 dimension of time exists, as you'd be frozen in 0-dimensional time otherwise and wouldn't be able to see anything.
Time movement
Contrary, we already live in 4 dimensions of space-time, of which the 4th dimension of space-time is the 1st dimension of time. You move through time constantly by yourself, and if someone where to move you, you wouldn't know that you've moved since you haven't moved yet or already did from your own perspective.
You'd need to exist in 2D time to be able to "experience" the entirety of any single string of 1D time, just like you'd need to be a 3D spatial being to see the entirety of a 2D paper/plane. Also, you would obviously not be aware if you were moved beyond your birth or death, as you wouldn't have a functional spatial body to interpret this.
Notice
This assumes that time and space are two separate phenomena that can be mixed in any given proportion, though resent research has proposed a theory that "space" might just an illusion of time, aka. that what we call "dimensions of space-time" or "dimensions" in general is just one big ol' load of bull.