Deep cycle batteries have a smaller number of thick plates.
Starting batteries have a larger number of thin plates.
Maximum amperage is a function of plate surface area. So more thin plates allow for more surface area and thus more amps...very useful turning over a big truck diesel.
Thicker plates allow you to take the charge down lower with less long term damage...very useful for deep cycling low to moderate house loads.
A 2000w inverter will be pulling less than 170amps
A 6-7liter diesel may be pulling 700-1000amps when starting but only for a few seconds
6v golf cart batteries are true deep cycle batteries.
The 12v trolling motor/combo batteries are relabeled starting batteries.
So for the same amp-hr rating, you won't see much difference initially but if you really use the capability, the available amp-hr in the starting batteries will drop more quickly as they wear out. If you only rarely boondock, you may never notice.
You can use deep cycle batteries for starting and it will cause them no damage. The issue is you will need more of them to develop enough amps. Quite common on cruising sail boats where you are turning over a small 20-40hp motor. It doesn't take a lot of amps, so the battery bank set up for house loads has plenty of cranking amps to turn over the small motor.