LOC basically lets you take output from speaker wires and covert to RCA - mostly used when adding amps to OEM Head Units like ours which do not have RCA outputs. There may also be some additional features on some units like bass boost or subwoofer control or minor EQ options. There are also options to take signal from OEM amped systems like the RAM Alpine setup where you have to pull the signal back from the oem AMP to get the full range/signal.
DSP is a Signal Processor, that typically be default also includes LOC functions as well as the signal processing, high/low pass, equalization, chime control, delay, tuning, input/output flexibility, etc. They also usually have custom harnesses available for most popular vehicles which make installing simpler as your not hacking up your oem harness.
PAC is the LOC you need if you have an RAM OEM Alpine Powered setup. If you just have the basic non-amped setup then any of the LOC's or similar would work to add a Sub or amps, etc - however an active/powered LOC is better than a passive, always.
DSP is a step up in control and flexibility - two most popular are the Rockford Fosgate DSR1 and Axxess AX-DSP, which basically do the same functions with a few minor differences. Comes down to personal preference, but in general the simplest comparions is that the DSR1 is geared more toward the professional/competition user while the AX-DSP is geared more for the enthusiast/audio shop installer usage.
I chose the AX-DSP, but you can't go wrong with either if you need a DSP. There are a few members here who have the DSR1 as well you prob find some reviews/info on those.