Lead acid batteries are normally charged with a three phase charger.
First phase is constant current, typically 15% of AH rating. AGM and gel cell can take higher phase one charge rate.
The constant current continues until battery voltage reaches an absorb level, typically about 14.3 vdc for a 6 cell 12v battery.
The second stage is holding the battery at absorb voltage until charge current tapers off to less then 3% of AH rating. The battery is considered fully charged at this point.
The third stage is a maintance charge where voltage is allowed to drop to about 13.2 vdc for a 12v lead acid battery.
The chart you are showing are just battery voltage profiles for a given manufacturers battery held at a constant charging current. Allowing the battery to go to the listed voltage level at full charge will damage battery.
There is an equalize phase in some chargers. This is to correct cell charge imbalance by doing a controlled overcharge of the battery. Typically done at 15 to 15.5 vdc for a 12v lead acid battery for a couple of hours. You don't want to do this for a sealed lead acid battery as it will result is high pressure build up in battery and cause the safety vent of battery to expel hydrogen and oxygen resulting in water loss which cannot be replaced in a sealed battery. The process is hard on the battery and should only be done when a significant difference in charge state (specific gravity of electrolyte) is observed. Again should not be done on a sealed battery.