How is the difference between them characterised in physics?

It seems like it would be hard to distinguish from the point of view of a 4D unit vector XYZT if T was massively larger. Is it distinguished because it's special or is it just distinguished just because the ratio to the other values is large.

Imagine if at the big bang there was stuff that went off in Z and XY and T were tiny in comparison? What would that look like? Part of me says relativity would say there's no difference, but I only have a slightly clever layman's grasp of relativity.

The difference is this: in regular 4D space, the distance between two points, (X1 Y1 Z1 T1) and (X2 Y2 Z2 T2) is (X1-X2)^2 + (Y1-Y2)^2 + (Z1-Z2)^2 + (T1-T2)^2), similar to 3D distances you may be more familiar with.

However, this is NOT the case in Special Relativity (or in QM or QFT). Instead, the distance between two points ("events") is (cT1-cT2)^2 - (X1-X2)^2 - (Y1-Y2)^2 - (Z1-Z2)^2. Note that this means that the distance between two different events can be positive, negative, or 0. These are typically called "time-like separated" (for example, two events with the same X,Y,Z coordinates but different T coordinates, such as events happening in the same place on different days); "space-like separated" (for example, two events with the same T coordinate but different X,Y,Z coordinates, such as events happening at the same time in two different places on Earth); or light-like separated (for example, if (cT1-cT2) = (X1 - X2), and Y, Z are the same; these are events that could be connected by a light beam). Here c is the maximum speed limit, what we typically call the speed of light.

This difference in metric has many mathematical consequences in how different points can interact, compared to a regular 4D space. But even beyond those, it makes it very clear that walking to the left or right is not the same as walking forwards or backwards in time.

Edit to add a small note: what I called "the distance" is not exactly that - it's a measure of the vector that connects the two points (specifically, it is the result of its scalar product with itself, v . v). Distance would be the square root of that, with special handling for the negative cases in 3+1D space, but I didn't want to go into these complications.