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Battery life

What is the difference bewteen 650mah and 900mah how long will the battery last me between charges?

That is a completely subjective question. (but more on that later)
If you want the nuts and bolts of it, the scientific answer... read on!

A 650mAh battery will put out 650 "milliamps hours" (mah) of energy, after that it will need to be recharged. .
Let's say I have an eGo battery at 650 "mAh" and it is rated as 3.3 volts output, and I have a 3.2ohm clearomizer attached to it.
We will need to use Ohm’s law (which is a constant) to work it how long the battery will last. Ohm’s law states that the current drawn equals the voltage, divided by the resistance.

When we apply this to the 650mah battery and 3.2ohm carto the math looks like this:

The voltage of 3.3 is divided by the resistance of 3.2 ohms. 3.3/3.2 = 1.03 amps (not millimaps) – which is the current draw.

We then move the decimal place so we can compare that current to our 650mAh battery – and 1.03 amps becomes 1030 milliamps. (milliamps is actually 1/1000 of an ampere, so 1.03 amps is actually 1030 milliamps)

So we need to move the decimal to figure out, get it? I know, enough with the math right? Sorry, has to be done, so let's continue...

We must divide the 650 milliamps per hour by the 1030 milliamps per hour we just calculated and we get 0.63 of an hour, which is just under 38 minutes.

This does not mean that your e-cig will only last 38 minutes from the moment you charge it, it simply means if you could hold the button down and fire that clearo for a solid 38 minutes you'd drain the battery of all of it's charge, but since you cannot so this, you have to add up your "puffs"

How many times in an hour do you press that button? How long do you press the button?

Do you change clearomizers and change ohms?  

All of this determines how long the battery will last between charges.  If you are a long toker or use lower ohm coils.. it won't last as long.

Vendors generally say a 650mah battery will last 4-6 hours but it might be a lot more.. or a lot less depending on your style of vaping.

Get a higher mah battery and you need to charge it less often, get a battery with a higher voltage and you'll charge it more often and maybe even more with a twist or varibale voltage battery.

The point here is no one can tell you how long a battery will last between charges, it's all about you and what you use.

Also, as batteries lose the ability to chemically create new electrons it will no longer be able to hold a charge, this is battery law based on the chemistry used in the internal battery, over time, your battery will lose it's ability to recharge and you'll have to get a new one.  No different than rechargable AA batteries that have to be tossed once in a while.

The average lifespan of a rechargeable battery is about 6-12 months, with the longer the time frame the less your battery capcity will be, so on day one if you get 6 hours of life, after 6 months you may get 3 and after 9, 1 or 2 until it stops holding a charge.