Yes. There is a relation and the explanation is little long
Quoting from What is C Rate?, C Rate or Charging rate is defined as
C-rate is a measure that governs at what current a battery is charged and discharged. At 1C, a battery rated 1,000mAh charges at a current of 1,000mAh. In an ideal world the battery would be fully charged in 60 minutes. At 1C, the same battery discharges at 1,000mA.
Your "different" charger is probably charging at a higher C Rate and hence faster charging. Pushing higher current (to an extent) will expedite charging but not necessarily. For a detailed understanding, see this, which explains various stages of charging and a relevant extract
Increasing the charge current does not hasten the full-charge state by much. Although the battery reaches the voltage peak quicker, the saturation charge will take longer accordingly. With higher current, Stage 1 is shorter but the saturation Stage 2 takes longer. A high current charge will, however, quickly fill the battery to about 70 percent.
(Voltage is not to be misunderstood with the capacity of battery. Accepted answer here explains it well App showing battery charge based on its voltage. Fully charged our charge state indicator on mobile UI refers to voltage not capacity)
Since the battery is not really charged fully (at higher C Rate), it would discharge faster compared to a battery charged optimally using the OEM charger (lower C Rate) (actual discharge is related to capacity, which is lower in the former case)
The relation between charging and discharging rates is further clarified as (emphasis mine)
The battery capacity, or the amount of energy a battery can hold, can be measured with a battery analyzer...When discharging a battery with a battery analyzer capable of applying different C rates, a higher C rate will produce a lower capacity reading and vice versa.
As a thumb rule (with exceptions) slower charging results in slower discharge all other conditions being same. Related, quoting from BU-409: Charging Lithium-ion
Manufacturers of these (Li-Ion) cells recommend charging at 0.8C or less to prolong battery life.