The manual and the charger interface are way too complex for the task intended and eager to show options instead of doing the job right.
The charging algorithms for Gel and AGM are the same. The flooded/wet batteries differ somewhat in the final target voltage.
If you charge flooded as AGM you risk mildly overcharging it. Bad if you leave it connected to the charger for weeks or months, otherwise it is OK.
If you charge AGM as flooded you will get it somewhat undercharged, e.g. 90-95% instead of 100%. On the other hand, the battery will live somewhat longer if left alone with the charger.
If it is cold (sub-freezing) flooded and AGM behave more or less identically.
So much about differences between the lead-based batteries.
Lithium are somewhat different - they don't like being tricle charged so the charger has to completely cut off after the battery is considered charged. In contrast, lead-acids of all types like to be "floated" (left at 13.4 - 13.6V in order not to lose charge and/or being periodically topped up.
If you need a once-off charging of a flat battery, you can disregard all the differences and charge at whatever algorithm you want as long as it is nominally 12V.
How these differ:
All lead-acids car batteries are heavy. Lead is notorious in this regard. The battery pictured above is ~20kg / 45lbs.
If no bragging labels say "AGM", it is flooded. When gently shaked it makes splashy noises.
AGMs wear bright labels saying "AGM". They are completely silent when shaked.
Gels are not used in cars, but can be found in UPS devices, house alarm systems and big powered toys. If you find a battery in a place like this, it is gel.
Lithium-whatever batteries are lightweigth, Li is the lightest metal. A battery with the same size like the one in the question will be 4-7kg. It will also have a big shiny label saying it is Lithium-something.
Lithium batteries of comparable capacity are still expensive compared to AGM. Li batteries of comparable SIZE are even more expensive (and more powerful as well).
