Hi everyone.
Power MOSFETS do consist of many little MOSFETS connected in parallel. These are called "cells". For given die dimensions, companies will try to fit as many cells as possible (they connect in parallel so as to drop the drain - source resistance), while keeping a reasonable gate capacitance. What changes between companies is the cell structure (almost every company has patented their own - VMOS, SIPMOS, HEXFET etc), which will finally determine the gate capacitance as well.
As for how the "gate capacitance" charges, it does so pretty much like a capacitor (the structure metal/polysilicon - SiO2 - Si, IS a capacitor), but does not follow exactly the curve. That's because there are other parasitic capacitances (gate - source, gate - drain, gate - body etc.) which also charge giving a slightly different curve.
You might want to check out here:
http://www.powerdesigners.com/InfoWeb/design_center/articles/MOSFETs/mosfets.shtm
for a more descriptive presentation on the topic.