PRP versus DLR
I think you understand the basics.
There are two different ways to get media fault tolerance in a ControlLogix EtherNet/IP network, and each of those modules supports one of them.
The modules with an "R" at the end of the part number support
Device-Level Ring (DLR).
DLR devices use a special "2-port switch" connected in a daisy-chain ring that self-heals a single link failure very fast. DLR was developed jointly by RA and Cisco, cooperating and documenting through ODVA (Open Device Vendor Association) committes. DLR is well supported both in ControlLogix and CompactLogix as well in smaller devices like VFDs, servos, and I/O adapters.
The modules with a "P" at the end of the part number support
Parallel Redundancy Protocol (PRP).
PRP is more like a "redundancy" system: there are dual links between dual switches that send frames at the same time and use the one that arrives first. It's an IEC standard, rather than something specific to industrial controls.
Adoption and use of PRP is less common in ControlLogix based control systems; 1756 and FLEX 5000 are the main devices that support it. No CompactLogix controllers support it.
"Why would I use one instead of the other ?" is a question I'm not sure I can answer personally because I've never built a PRP system. In general I don't think you'd use it unless you need very high availability networking with a ControlLogix Redundancy system, and have the hardware, training, and maintenance budget to make it worthwhile.