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It is the total cycles in terms of percentage discharge and charge totalled to full cycles, when discharge is to no less than 1/4 to 1/3rd and full charge is no more than 2/3rds to 3/4. Full discharges and full charges, elapsed time and elevated temperature all shorten life. Charge controllers actually disconnect the cell before its fully discharged and stop even trickle charging above a certain point. They vary on how well they are implemented and some "lock" out charging when a certain number of equivalent total cycles are reached. The Kindle keyboard has a controller/sensor in the cell pack and on the main board. It will eventually stop charging a cell even if it's not completely worn out (though that was a 10 year old cell).
The NiCd had a memory effect, also they could grow nickel dendrites that would short the cell.
The NiMH has no memory effect but is damaged by a level of trickle charge when "full" that's acceptable for NiCd.
Both self discharge, though some purer NiMH take a year, NiCd can take a week. Both will last almost indefinitely if stored discharged. The Lithium cells need stored at 1/3rd to 2/3rds and thus are often shipped at 2/3rds charge.
Lead Acid cells sulfate if left flat. They need to be stored dry (30+ years shelf life) or fully charged. It's a retrograde step that Lead Acid are now retailed "pre filled" with the sulphuric acid as they deteriorate.
NiCd and NiMH are destroyed if reverse charged often by a stack (6V, 9V, 12V etc battery packs) being repeatedly run flat (less than 1.1V per cell) as the cell that is discharged first is reverse charged by the others in use.
Lithium cells go on fire if reverse charged, or if it's attempted to charge a truly flat cell. That's why laptops etc have a cpu dedicated to the cells and measure the voltage of every cell in the series chain.
You can even cause single use lithium coin cells to explode or go on fire. The -ve terminal plate can be flung 20m away. I've photos.
It's technically possible to recharge Alkaline cells, but they can't be trickle charged when full and must not be charged when less than about 1/2 discharged, so no-one does it, as it makes more sense to use the rechargeable lithium cells.
Turbo charging of NiCd or NiMH is hazardous, though I only exploded one set of NiiMH designing the charger. It does shorten the life.
The batteryuniversity site is quite good, but not the whole story.
Don't buy battery versions of any tool or appliance where the mains is convenient. It's heavier for same power due to the batteries, less environmentally friendly (making cells and loss in recharging) and life may be only 12 to 30 months.
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