The myth of battery memory was always, on the very few occasions when it was checked and not put down to magic, found to be one cell in the pack being a bit weaker than its mates and not quite charging to the same level. This usually meant that it was fully discharged earlier, giving a very sudden performance drop, and the subsequent recharge didn't really improve matters. This all happened in the days of NiCad batteries, production methods are now more reliable. Having said that, over time and with use, the chemicals inside the battery, of whatever chemistry, will eventually cease to arrange themselves back in the same places, and the battery will eventually fail. With lead acid, all of the cells are in a single moulding, so, effectively, it all dies at once.
SLA require a regulated voltage, alkaline (NiMH, NiCad) require regulated current, so using the right type of charger is necessary to get the best number of charge/recharge cycles out of the battery.