Is time fundamentally different from space? Note: This is a rewrite of the original question, which was titled What would time be for 2D beings?

In my current, non-physicist's understanding, every instant of our three‑dimensional world is just another 'slice' of a four‑dimensional body. I don't mean that as an analogy, but quite literally... Obviously, it would not be a straight 'slice', it would still be bent and curved by gravity, speed and other relativistic factors. Is this wrong?
Also, both 'spacial' and 'temporal' dimensions are — in my mind — fundamentally the same thing, given different names because we experience them differently because of our nature. I've had people explicitly say in the comments that this is wrong and that time and space are not the same 'type' of dimension. I'd like to understand what are the fundamental differences.

In my original question I used these two assumptions of mine (that space is a slice of time and that all dimensions are fundamentally the same) to make an analogy.
I noted that taking two-dimensional slices of a three-dimensional body — just as a slice of four‑dimensional time is three‑dimensional space — and displaying them is rapid succession looks like a bunch of matter that is changing over time (like in this brain scan below).  

Assuming all dimensions, temporal or spatial, are fundamentally the same, would that mean that for a hypothetical two‑dimensional being time would be the thrid dimension, not that fourth?
The same question in a more general form: for any $n$‑dimensional being, would time for it be the $n+1$ dimension?
In particular, what would time be for a being living in a hypothetical fifth dimension?
 A: I think you are correct for this hypothetical 2D being. However, you should be aware that time is not just a dimension. In space-dimensions, you can in principle move freely forward and backward, while in time, your motion is fixed.
With respect to the brain scan: this way of visualisation is chosen for simplicity. A regular 3D image, where you can look at any depth you want, will give a clearer image of what is happening in this third dimension. Some information is a bit lost for the observer: you clearly see structures in the x,y-plane, but for vertical coordinate, it is not that obvious.
Some bit off-topic reading material may be: http://en.wikipedia.org/wiki/Flatland
A: My take is time is indeed fundamentally different from space, as, for example, time enters the invariant interval with a different sign: $(ds)^2=(dt)^2-(dx)^2-(dy)^2-(dz)^2$.
A: Time and space is a way of splitting the set of all space-time events into two sets: 
Space is the family of sets of space-time events simultaneous with one another, with each element of a set paramaterised by three real numbers called the space coordinates; each set paramaterised by a real number t called time.
Alternatively, time is the family of sets of space-time events that aren't simutaneous with one another, each element of a set parameterised by a real number t; each family paramaterised by three real numbers called the space coordinates.
On the one hand space and time are identical in both being partitioning functions; on the other, they're different partitioning functions.
A: The sign is actually metric tensor $g_{\mu\nu}$,It takes the value $-1$,$1$,$1$,$1$ only in Minkowski space time.In here you may find what you need http://en.wikipedia.org/wiki/Metric_tensor
