If you're of a more mechanical bent, you might find it helpful (at least for amps and volts) to think in terms of an analogy based on fluid flow.
Voltage is the electrical
equivalent of fluid pressure, and current
(amps) is the equivalent of fluid flow rate.
Say you were building yourself a house off grid, but you could run a hose to the site from a water
reservoir up the hill, and needed a way of pressing clay into bricks.
If the reservoir was 50 feet higher than the site, you would need lots of water
because the pressure would not be very high: you would need to build a hydraulic cylinder of large diameter, to have a large piston area.
If the reservoir was 500 ft higher, providing ten times the pressure, you could build a cylinder with a piston one-tenth the size and still get the same squeeze force.
In both cases, the cylinder stroke would be the same.
To supply enough water to press the same number of bricks in a day, the low pressure option would need a big diameter, thin walled hose. The high pressure option would use a small diameter, thick walled hose, and use one tenth as much water, per day.
The high pressure is like higher voltage. The associated low flow rate is like lower amperage, or current
The fluid flow rate would probably be measured (in the US) in gallons per minute.
Which corresponds to amps.
The AMOUNT of water used in a day would be measured in gallons.
Which corresponds, conceptually, to amp.hours, or amp-hours.
You'd need to know this to work out if the reservoir was BIG enough.
The only time you might calculate the fluid equivalent of amps PER hour (gallons per minute PER minute) would be if you were interested in an unusual application where the flow rate had to change rapidly.
Maybe you're building a hydraulic cylinder to launch planes off the deck
of a carrier, and you need the flow rate to build steadily during the course of a single
stroke from zero to 1000 gallons per minute. If the stroke took one tenth of a minute, that's a flow acceleration rate of 10,000 gallons per minute, PER minute.
In electrical terms, the conceptual equivalent is amps PER hour. And there is virtually no useful application for such a concept
on a boat.
Much the same thinking can be applied to watts as to amps, on a boat. This is because we're dealing (generally) with a constant voltage.
- - - -
Watts is a way of measuring how fast we can do a given amount of work. if we're pressing bricks, it gives us an idea how many bricks we can press in an hour.
We could achieve the same work rate with the high pressure, low flow option as the other way; the rate of doing work with fluid is simply Pressure times Flow Rate
In the electrical case, the rate of doing work is watts, which is volts times amps.
Given that the DC volts on a boat will generally be 12 or thereabouts, we can therefore apply the same reasoning to watts as we do to amps. There is no useful application for watts PER hour.
Watt.hours, on the other hand, is
useful and relevant. It's a measure of work needing to be done (bricks to press) or work done (bricks pressed).
Because watts is a measure of rate of doing work (bricks pressed PER hour): if we multiply watts by hours, we can work out how many bricks we pressed (in that number of hours).
On a boat, watt.hours will tell us how many sinkfuls of water we can heat, or fill, or pump out. On a big boat, will tell us how many times we can raise the anchor
, and/or the mainsail
It's a measure of storage
capacity, and so is amp.hrs.
(Because the other relevant variable, voltage, is essentially constant)