So a 4000mah battery pack (with a current limit of 1000ma) will charge up your battery as slowly as a 1000mah battery pack (with a current limit of 1000ma).
Thanks!

Ok so for example, is there any way to get an estimate of how long it takes to charge up various capacity PowerBanks from the wall-wart/mains, given that the wall supplies are always 1000 mA? So how long to charge a 1000 mAh powerbank? What about 2000 mAh, 3000mAh or 4000 MAh? I thought it would be the capacity of powerbank divided by the charge current:
1000 mAh / 1000 mA = 1 hour to charge. (charging 1000 mAh bank with 1000 mA source)
1000 mAh / 500 mA = 2 hours to charge. (charging 1000 mAh bank with 500 mA source)
4000 mAh / 1000 mA = 4 hours to charge. (charging 4000 mAh bank with 1000 mA source)
At this point, my 4000 mAh powerbank has been plugged into a 1000 mA mains source for close to 8 hours and still blinking the 4th of 4 LED's on it (which indicate how full the powerbank is). The other identical one that came in this 2-bank package has already charged (all 4 LED's are solid).
I guess because the charging curves aren't linear, and there are interactions between the charging circuit and the battery, and there is a "leveling off" of the curve near the capacity of the bank, that it will slow down the charge rate? So you can't do simple calculations like that?
Same would then go for when you want to charge up the phone... So if your phone has a 2000 mAh battery, and your powerbank has 4000 mAh battery, due to inefficiencies you cannot get 2 full charges of your phone battery from the powerbank? Or if your phone has a 1000 mAh battery, you cannot get 4 full charges of your phone battery from the powerbank?
One other thing... the battery sticker says 14.8 Wh. So if I am drawing 1 A of current at 5 V from the powerbank (output) to charge my phone, then it is running at 5 W (1 A x 5 V) and I can sustain this for about 3 hours ... since 5 W x 3 h = 15 Wh. Technically then would I not have only drawn out just under 3000 mAh from this supposedly 4000 mAh powerbank?
Stated another way.... 14.8 Wh = 2960 mAh as per this calculator:
https://milliamps-watts.appspot.com/ 
The only clarity I think I have found somewhere has to do with the fact that the cells are 3.7 V and while the voltage needs to be boosted to 5 V for output, and something about efficiency also being 80-90%. So between 3.7 to 5 V, and 80-90% efficiency, is the reason these calculations are all off.
Basically, if I take 5/3.7 x 2960 = 4000 the math makes sense again.
I guess 4000 mAh is the capacity at 3.7 V, which multiplied gives 3.7 V x 4 Ah = 14.8 Wh. I shouldn't be using the 5V at all.
I think I answered my own question.... The confusion stems from the fact that the Li-Ion battery ratings are all based on the 3.7 V voltage of the cell itself, whereas I am treating the entire PowerPack as a 5V source and assuming the 4000 mAh is being delivered at 5V... whereas in fact it is what is being delivered at 3.7V.
Essentially, 4000 mAh @ 3.7V = 2960 mAh @ 5V (and that is 100% efficiency in conversion of voltages). To add to the problem, what happens when it goes into the phone and has to then be converted to something that will charge the 3.7V battery in the phone.... Confusing even more!
