GH is general hardness. It's a measure of divalent metal ions. In practice this means mainly calcium with some magnesium and trace amounts of other metals. (Source of information - younger son who used to work for a water testing company)
There are around half a dozen different units of measurement for GH. It's far worse than inches/cm. And they can have different names for the same unit. Fish keeping uses just two of those units.
dH, also known as German hardness
ppm, also known as mg/l calcium carbonate.
So GH is calcium and magnesium in the water and dH is one of the units of measurement used for GH.
Fish profiles use one or other of these units and the calculator section on here has a converter to change back and forth. Some US water providers use the unit grains per gallon - that's in the converter as "US hardness".
Yes you can buy test kits for hardness. For example, API make one.
The word hardness is reputed to have started because water with lots of calcium makes it hard to get soap to lather. Though why soft was chosen for water where soap lathers easily is anyone's guess.