Will charging a phone with a different USB *cable* affect the battery life?
Moto X Play supports fast charging, though this review says a fast charger is not supplied with it, maybe they supplied it subsequently
Fast charging needs to be supported by the USB cable as well. The D+ and D- pins of the cable negotiate the charging voltage and current with the device, in tune with the charging circuitry in the charger (see Overview of USB Charging for more details
If a cable/ charger that does not support fast charging is used, there is no harm caused -  charging will be normal charging instead of fast charging. In the case of cable, it is because it may not be designed to carry adequate fast charging current, which is usually higher than normal charging


Additional Information  you may like to refer:


How does fast charge work
How to choose micro USB cable for my device