Deep cycle conventionally means thick plates, designed to last a long time. A thick plate cannot supply as high an impulse current as thinner plates, so an SLI (Starter-lights-igntion) battery uses thinner plates.
A "dual purpose" battery uses plates somewhere in between.
What do thick and thin mean? Varies with the maker.
And the makers will all tell you, you can use deep cycle batteries for starting with no problems, as long as your battery bank is large enough to supply the impulse power your starter needs. i.e., you don't use a 50AH rated deep cycle battery as a starter for a big diesel. But a 400AH bank won't blink at the power need. (Depends on what you call "big", I know.) And on the other hand...yes, I've used a 17AH AGM backup battery to start asmall diesel. It didn't mind in the least, but I would use it that way on a daily basis.