The voltage needs to be accurate. But you can get something with much higher mAh rating (and a higher output current - Amps).

• A higher mAh battery will just be able to charge your battery more times (or for longer), and won't damage your battery.
• Higher Amps will allow your phone to charge faster (phone will draw only the current that it can safely handle. Lower Amps will allow your phone to charge, but slower)
• Wrong voltage however is a bad idea - check the voltage rating on your OEM charger. I suspect it will be 5v output. The 3.8v you see on your batter is what your battery will output to the phone when in use

 

Nearly all cellphones accept a nominal 5.0 to 5.5 volt input.

The phone's internal charger regulator chip is what determines the charging voltage and usually the maximum charging current. That is, up to the limit of what the source can provide.

If the source is a puny 0.5 amp output, then the phone's battery will just barely get a trickle charge assuming that 0.5 amp is provided at 5.2 volts approximately.



Consider car chargers. They have a source capable of hundreds of amps, but the plug in charger adapter will limit that to about 2 amps or so. Again, it will be regulated down in voltage to about 5.2 volts.

.... hope this helps a bit.


one more thought....

ie, I am looking right now at a charger module on my desk, it states "Output 5 volts ~ 1 Amp". Using this on my S5 just about doubles the required charging time because the initial charge rate can be no more than 1 amp. However, the S5 charging rate backs off after a few minutes to prevent overheating the battery. So, instead of double the normal 90 minute charge time for the OEM 2.2 amp charger, it takes about 120-140 minutes to charge the phone. Depends on how discharged the S5 is.

 

Not really...
in fact, those are two critical parameters that distinguish a good charger from an average one.

You want a portable battery to be able to charge your battery up a few times (if you are unable to get to a power outlet for a day or two), so higher mAh is important

Also, you want your phone to charge up quickly, so a sufficient current rating is important (if you phone can charge at 1.5Amps, your phone will charge very slowly if your portable charger can only output 750mA)