What are the core differences between the paradigm roles?

I'd like to understand the paradigm system in Final Fantasy XIII from a high-level perspective a little bit better, but I'm having trouble telling the different paradigm roles apart.

What are the main differences between the roles? Is there a main benefit to using one role over the other?

There are six roles: Commando, Ravager, Medic, Sentinel, Synergist, and Saboteur.

Commandos (COM) are your fighters. They attack with their basic weapons and they keep the chain gauge from draining, but don't increase the chain gauge much with their attacks. Most useful paradigms have at least one Commando, although there are some special circumstances where one might not be necessary.

Ravagers (RAV) are your black mages. They attack with elemental magic and charge the chain gauge a lot, but also cause it to drain more quickly. These are your primary offensive roles, and you want to have at least one in any paradigm that is intended to deal damage.

Medics (MED) are your white mages. They heal allies by restoring health and removing negative status effects. Use them to heal. There isn't too much more strategy than that. Sometimes you can stick a Medic in an otherwise offensive paradigm to try to sustain longer, but that's generally less effective than switching back and forth from a pure offensive to a defensive paradigm.

Sentinels (SEN) are entirely defensive. They "aggro" the enemies, forcing attacks to target them or punishing enemies for targeting allies, and have much increased defenses. Use them to keep the heat off your other characters while healing. With a Sentinel and a Medic in the same paradigm, you're pretty much invincible.

Synergists (SYN) buff allies. Any buff you could cast on an ally will be cast by the synergist. You generally don't need Synergists for the whole battle. Instead, you want to start with a Synergist in your paradigm and allow him/her to buff you up for a while, and then switch that character to a role more focused on dealing damage to enemies to use these buffs. Switch back to a paradigm with a Synergist only when the buffs wear off.

Saboteurs (SAB) debuff enemies. They are the counterpart to Synergists, and should be used in much the same way. There is no advantage to having a Saboteur when the enemies are fully debuffed, so switch to another role once you are satisfied with how crippled the enemies are.

The total number of possible paradigms is just too vast to list all of them, but from my experience the only three I ever had to use were:

• Commando, Ravager, Ravager (Relentless Assault)
• Commando, Medic, Sentinel (Solidarity)
• Commando, Synergist, Saboteur (Bully)

Start with the last one to buff your team and debuff the enemies. Most of your time should be spent in the first one, in order to increase the chain gauge quickly and inflict maximum damage. Whenever you need to heal, switch to the second one for a bit, let your medic heal up your team, and switch back to the first one.

Overall, the system is a lot less deep than it seems at first. You can do most of what you want with very few paradigms, and it's rare for a battle to require any kind of special strategy.