"deep cycle" is another of those much-used and abused terms
A car battery is designed to be kept fully charged most of the time, and to be able to deliver high amperage for a short burst for the starter motor - it doesn't need deep-cycle abilities, so for cost reasons, they don't build it in!
For most renewable energy needs, a car battery will last a few weeks at most if "deep cycled" making them hopelessly uneconomic - you do need true deep cycle abilites.
In practical terms, that translates to the most cost-effective being either flooded deep cycle lead acid batteries, or advanced glass mat sealed batteries -
Flooded cell batteries are tolerant of overcharge, but will need topping up from time to time, and are not the best for really deep discharge (I'd never design to go lower than 50% discharge, and then only very infrequently)
Advanced glass mat batteries cost around 50% more, can be discharged down to 20% of their capacity, need no topping up, and will probably last at least twice as long as the flooded ones, but they really dislike overcharging, so you need a very good controller to feed them.
Manufacturers are coy about performance figures, but if you take a standard AGM battery, it will probably claim something like ~"300 cycles to 80% dod" (depth of discharge), which means you can take 80% of the power from it 300 times..........(if that's daily, that's a year!) - at lower discharge levels, the life extends considerably - it's a simple maths thing
300 cycles to 80% dod
or 2400 cycles to 10% dod - and pro rata!
As a rule of thumb, we design systems to take a maximum of 10% of the battery bank's capacity during the average day
Hope that helps a bit - it's actually a fairly complex subject!