The reason "deep cycle" has been used to mean so many things is that it doesn't actually mean any one thing. Given that they use the same chemistry as other batteries (and indeed you can get deep cycle classic lead sulfate, gel, solid, or whatever kind of battery you want) the difference is the thicker plates, and thicker connections between plates, and between plates and lugs.
Don't believe that a deep cycle battery shouldn't have CA or CCA. That is a lot of nonsense, because there are batteries intended for both deep cycle and starting. And frankly, if you put a lot of faith in an amp-hour rating, or any other rating, you're being silly. Manufacturers do everything from re-running tests to outright lying. Just because their test battery performed a certain way that doesn't mean yours will. Etc.
Finally, starting the IDI doesn't necessarily take a lot of battery. I had two sad old tired 650 CCA batteries and they started my truck fine, literally for years after I got the truck. Now I have two shiny new 850s and yes, it starts faster... but only just slightly. But I have a Nippondenso starter instead of the stock Mitsubishi, which I recommend to anyone shopping for a starter. Frankly, I think one shiny 850 would do the job, but extended cranking would risk overheating the battery, and a second battery doesn't add all that much weight.
There is way more depth to battery selection other then plate thicknes you have to get into the chemistry self discharge rates charging efficienes, discharge efficiencies, Absortion voltge, float voltage whether or not the cell type needs equalizing. How ever it is only tht complicated if you depend on them to run your house for your average consumer you can over simplify like you did, but make no mistake it isn't that simple.
Any manufacturer who gives miss leading specs finds them self soon out of the off grid market! Deal with repuitable companies and the batteries will perform within their tested window, and boy do we test them befor puting them into service! 10 grand is the average cost of a bank! you make damned sure you get what you've paid for!
FYI lead sulfate is the bad thing in the battery not the battery chem, Lead calcium, lead antimony, Lead selenium alloy plates (Determins self discharge rates and to some degree the level of gasing befor the absportion charge is reached), all use lead peroxide in the active paste, Nickle Iron use Nickle compound and a Patasium lithium hydroxid electrolyte, NiCad use patasium hydroxide.
You have Flooded lead acid (Typical in auto motive)
AGM is the upcomer due to its more robust design and ability to survive shock and vibration with added charge acceptance and high discharge rate
Gell is craptastical! Very picky charge voltage window and charge rate limmited and really dislikes high discharges
Exactly and thus not a true deep cycling battery (The term was rather precise as to its meaning back in the day, now days it is a miss leading sales gimmic), if it has a ca/cca it is a hydrid class and not a deep cycle.
I could have writen 3 pages worth of info but that isn't the nature of this thread, Kiss rule is what I was trying to keep it to.