From: somewhere in Massachusetts
In RL, the various classes of shiping can generaly be broken down as follows:
xAKL -small cargo ships w/limited endurance; more suited to intercoastal port to port ops; they usually had load/discharge capacity in the form of onboard booms and winches. They could load/unload via lighters. No inherent amphip capability.
xAK -larger cargo ships w/intercontinental endurance; suited to port to port ops; almost exclusively had load/discharge capacity in the form of onboard booms and winches. They could load/unload via lighters. No inherent amphib capability.
xAP -larger passenger ships, converted to load/unload troops; suited to port to port operations only, w/limited cargo capacity. No inherent amphip capability.
The above require port facilities and will not load/unload at a undeveloped dot hex.
TK -a tanker which can carry fuel and oil suited to port to port ops only. All tankers carried their own pumping machinery to discharge at a port. The port had pumping machinery ahore to load the tanker.
AO -a tanker which in addition to normal tanker ops, could refuel ships underway, due to enhanced communications and hose handling equipment.
The above, in all cases, can refuel ships in port.
AK (AKL) -cago ships, converted or special built to perform cargo ops 'over the beach'. In addition to normal cargo ops w/boom and winch machinery, these ships carried smaller boats, like LCVP , LCP or barges as lighters, which could carry cargo from ship to shore. Thus an inherent amphib capability.
AKA -Same as above with enhanced capabilities (more lighters) to rapidly discharge cago 'over the beach'.
AP -converted or special built troop ships which carried smaller boats, like LCVP, LCP, or barges to move troops ashore 'over the beach'. These ships were used as assault vessels early in the war.
APA -same as above with enhanced capabilities to rapidly put ashore troops. These ships came later in the war and were, along with the AKA, the primary USN first wave assault ship.
The above, in all cases can be used for conventional transport of troops, port to port.
LST, LSD, LCI, etc -special built amphib vessels with bow or stern doors, ramps, etc, to load/unload directly to a beach.
Notes: Amphibious TF's are 'combat loaded', having about 80% capacity as a convetional cargo or tranport load.
Ships prefixed with an 'x' were unconverted commercial vessels, used for miltary cargoes or troops.
I think that covers the major catagories. Please feel free to correct or add as I'm not familiar with all the smaller boat designations, such as LCVP, etc.