Battery health and charge cycles

I had a local Apple shop replace my battery in October 2015.

They replaced it with the last 4S battery they had on shelf and they only warranty the battery for 30 days.

I didn't aggressively test the battery, but it definitely lasted a minimum of 4 hours playing a video from M-GO in airplane mode and low brightness. But this doesn't jive with Apple's specifications for an iPhone 4S.

I installed an app called Battery Heath in January of 2016, and it reports a Cycle Count of 1258 (lifetime).

I am wondering if that's the cycle count of the individual battery or the iPhone 4S motherboard.

Additionally, I have noticed that Battery Health reports this battery as having a maximum capacity of 800 mAh, and sometimes jumps up to 900 mAh, but the original design scenario is supposed to be 1430 mAh.

I bought a new Stalion battery from Amazon and it failed the moment I unplugged the charger (at 47% is when it stopped charging), but during the charge cycle, it reported 1420 mAh. So it seems like there is some truth to the capacity reporting of Battery Health.

I regret failing to look at the cycle count (lifetime) field, and now that the Stalion battery has failed, I can't assess the scope of cycle count myself until I receive a replacement battery.

Hey, thanks for your help/wisdom/knowledge, and for taking time to help someone in need.