You're confusing units.
mAh - milliamp-hours. The base unit is amp-hour, which is a measure of battery capacity. One amp-hour means (in theory) it can provide one amp for an hour. 10Ah would be ten amps for one hour, or one amp for ten hours.
mA - milliamps. The base unit is amp or ampere, which is a measure of current. There's a fancy explanation using coulombs and flax but basically it's how many electrons are flowing through the wire.