Another 12v battery question

I bought 2 12V 22AH batteries for my wheel chair that run down quite quickly. The wheel chair has a battery voltage indicator on it and it always shows full charge but as soon as you dry draw power from them, it shows low battery then goes back to full when not drawing power, then abruptly drops down past the yellow to the low red lights, even though you're not drawing power, except for the monitor circuit. At this point, it barely moves, take a while to 'drive' it to the charger.
I believe these batteries were intended to used to jump start a car and such, but not for continuous draw over time, They gave me another set of batteries, different brand, that are working out better and so far it appears that as the batteries drain, reading the indicator on the wheel chair shows the voltage dropping and staying dropped. one step at a time.
I'm happy with the company, but wonder what the big difference in batteries is, I think they said that the new set is Deep Cycle, but what is the first set and what's the difference in construction?

Deep Cycle batteries have a thicker plate construction that better tolerates discharging to a low level of charge as compared to a standard vehicle battery.
Vehicle batteries have thinner plates optimized to deliver maximum starting current but have a shorter life if repeatedly discharged to a low level. Your first battery may have been a vehicle type used for starting small engines, such as riding lawn mowers,etc.

Note that even a deep cycle battery should be discharged no lower than about 45% of its capacity for optimum life.
So recharge you wheel chair whenever you can rather then letting in run down to the red lights point.