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So is it simply, 4 dimensions of spacetime, 3 spatial and a time dimension, and these dimensions are not cleanly differentiable, but rather form a 4 dimensional "mesh" we refer to as spacetime?

There are other physical dimensions that are worthy of consideration and eventual incorporation into a possibly grander understanding of relativity. They have apparently been all held constant for SR which does not describe particles or fields accelerating with respect to each other. These are normally fixed (for a vacuum) and embedded within constants such as the fine structure constant or vacuum permittivity. Some examples would be:

Electric Charge

Temperature

Capacitance

Inductance

Resistance