ok so if I have this right milli Amp hour= mAh, Whr = Watt hour, and v = Volt is charge capacity? Where is potential discharge or work capacity and V is the rate at which the "work" is being done?
The battery life of your iPhone depends on it's usage. 1440mAH or 1560mAH refers to the basic term that if your phone uses 1mA per hour(i.e 1 W/v) it can last for 1440 hours. But the usage will depend on what all software you are using. Like mobile network and heavy graphic intense games will use more power, applications that don't require a lot of processor power to work,(such as a clock) will not take so much amount thus you will have a longer battery life.
There are various articles explaining this online, if I find a suitable one I will post it in an edit soon.
You have a skewed understanding from what I can tell. This may be a bit overkill, but some simple physics couldn't hurt. Let's start with the basics:
Voltage, measured in Volts (V), is the potential energy of electrons between to points. It is analogous to pressure in pipes.
Current, measured in Amperes (A), is the rate at which electrons flow, equivalent to 1 Coulomb per 1 second (1 C/s, 6.241×10^18 electrons per second). It is analogous to the flow rate of water in pipes (the volume of water that flows by per unit of time, e.g. Litre/second).
Power, measured in Watts (W), is the rate at which electrons flow, multiplied by the potential energy of each electron. It is equivalent to a Volt Ampere (VA). I.e. 1 Amp of current at 1 Volt potential is 1 Watt of power.
Energy, measured in Joules (J), is the product of the power multiplied by the time over which it was applied. It is equivalent to 1 Watt Second (WS). I.e. 1 Watt of power being consumed for 1 second is 1 Joule.
Charge, measure in Ampere-Hours (Ah), is the product of the current flowing by how long it has been flowing for, regardless of voltage.
Multiplying charge by voltage gives you the Voltage-Ampere-Hours (VAh). From above, we can see that Voltage-Amperes are the same as Watts, so this gives us Watt-hours (Wh). Watt-hours are a measure of power, multiplied by a measure of time, which we've also established is Energy
A milliampere-hour has 3 parts: "milli" denotes that the quantity is 1 thousandth of the base unit, "Ampere-hour", which is a unit of charge.
At the same voltage, charge is proportional to energy stored in a battery.
We can run the simple calculations:
3.8 V * 1440 mAh = 3.8 V * 1.4 Ah (milli denotes 1/1000th) = 5.32 VAh (multiply the values) = 5.32 Wh (VA is the same as a W) = 5.32 Ws * 3600 (3600 seconds in an hour) = 19,152 Ws = 19,152 J (Ws are the same as a J)
3.8 V * 1560 mAh = 3.8 V * 1.56 Ah (milli denotes 1/1000th) = 5.928 VAh (multiply the values) = 5.928 Wh (VA is the same as a W) = 5.928 Ws * 3600 (3600 seconds in an hour) = 21,340.8 Ws = 21,340.8 J (Ws are the same as a J)
As you can see, the second battery holds ~11% more energy than the first.