The figures "2000 mAh" and "2600 mAh" describe the amount of electrical energy that a battery can produce. That electrical energy is also called the "capacity" of a battery and it is a guideline for how long a battery will last before it is "drained" or depleted. The unit "mAh" stands for "milliamp-hours" and it is the standard way of measuring small-battery capacity.
A battery provides voltage and current to an electrical circuit. Voltage is the amount of stored, or potential, electrical energy that is available and it is similar to the hot water that is contained in a water heater. Current is the moving, or kinetic, electrical energy that originates from the voltage source. Current is similar to the hot water that flows from the water heater, when a faucet handle is turned. Most electrical circuits require a fixed amount of current and will "draw" that amount from a battery, until the battery is depleted.
Amps and Milliamps
The term "amps" is short for "amperes," which is the standard unit for measuring the flow of electrical current. The unit "milliamps" (abbreviated "mA") is derived from amps and it is used for measuring current in small electronic devices such as computers, cell phones and radios. In comparison, one amp equals 1,000 milliamps.
The capacity of a battery is determined by the amount of current that it can provide to a circuit, in a single hour. For small batteries (AA, C, D, 9V and others), the capacity is based upon "milliamp-hours," which is abbreviated by "mAh." The figure "1 mAh" means that a battery can provide 1,000 milliamps of current to a circuit for the duration of one hour -- before it is depleted.
The speed of battery depletion, or "discharge rate," depends on the amount of current that a circuit draws. The discharge rate of a battery is similar to the "drain rate" of a water heater. If a faucet is fully-open, the hot water in the water heater drains quickly. If a faucet is only slightly-open, the water trickles out and the hot water in the water heater drains slowly. In relation, a 500 mA circuit will deplete a 2,000 mAh battery faster than a 100 mA circuit, because "500mA" is a greater discharge rate.
Differences in Battery Capacity
The 2,600 mAh battery and 2,000 mAh battery are probably the same voltage, but the 2,600 mAh battery will "last" longer. Because of the greater capacity, the 2,600 mAh battery may also be physically larger. The amount time that a battery lasts before depletion is found by dividing the capacity by the discharge rate (circuit current). For example, if the 2,600 mAh battery is connected to a circuit that draws 500 mA, the battery will last about five hours (2,600 mAh divided by 500 mA equals 5.2 hours). If the 2,000 mAh battery is connected to the same 500 mA circuit, that battery will only last about four hours (2000 mAh divided by 500mA equals 4 hours).