Typical Marine batteries are "Dual Purpose" so they "technically" did not lie to you. They are just crappy Starting Batteries and Crappy Storage Batteries at the same time.
Starting Batteries are designed to give up huge amounts of amps (hundreds) in a short period of time (measured in minutes). The plates are thin and "waffled" so there is a large surface area to launch electrons from. They recharge quickly because the large surface area has lots of holes for the electrons to find and "be happy."
The downside is they have very little staying power; not very much capacity beyond the surface.
True Storage Batteries (Deep Cycle or Solar) have THICK FLAT surface plates that have LOTS of holes for electrons to live but they are deep inside the lead. It takes a time (and power) to push the electrons (who are happy on the surface) out of their homes into holes deeper inside.
Once filled to capacity a storage battery holds many times the electrons than an equivalent sized starting battery.
The downside to a deep storage battery is it can't "give them up" as easily as the electrons deep inside can't get to the surface fast enough to provide high current.
For inverter use two 12 volt or 2 6 volt Deep Cycle batteries are optimum for a 1000 Watt inverter (what I have).
For a 2500 Watt Inverter 4 12 volt or 4 6 volt batteries are normally found.
I recommend these:
With free shipping they will give you the most bang for the buck (310 AMP HOURS) in a Gel Battery. While many say 6 volts are better, I like 12 volt batteries due to the ability to lose one and still have 12 volt power and you can keep camping.
Lose a 6 volt battery and the trip is over.