Les Jacobins
The Jacobins are the leading party. Begun as the Jacobin Club, its members are the closest to Robespierre, and it's chiefly members of that party which make up the Committee of Public Safety. However, there are relatively few Jacobins in Paris, and they rely on the larger, low-class group, the Sans-Culottes. Their ideology is political extremism in the service of the Social Contract and equality of all before the law... but chiefly, most of them are simply self-serving, seeking power.
Les Sans-Culottes
Named for the long trousers worn by the typical working man, the Sans-Culottes support rights for the lower classes rather than the bourgeoisie. Simple and straightforward, most of them simply want the populist government the Jacobins promise, and agree with many of the Enragés as well. Bottom line: they're the political infantry of revolutionary France. They have the numbers, and it's their support that truly underlies the aims of the other parties.
Les Enragés
In contrast to the other two groups, the Enragés have aims which are chiefly economic rather than political. And in the terrible economic climate of 1794 Paris, they're justified in this desire. They push for:
* Price controls on grain
* The assignat (banknotes issued by the National Constituent Assembly earlier in the Revolution) as the only legal tender
* Repression of counterrevolutionary activity
* A progressive income tax
They too have support from the Sans-Culottes.
**NEW**
The Committees and the National Guard
The Committee of Public Safety
This extremist committee, headed by Robespierre, take care of denunciations, trials, and executions, and are responsible for thousands of them. Members of this Committee are all Jacobins.
The Committee of General Security
Basically, this is the group in charge of everyday policing. They manage the National Guard and take care of the minutia: how exactly to track down those the Committee of Public Safety denounces. Unsurprisingly, there's some resentment between the groups. The Committee of General Security also has to take care of mundane law enforcement in the city. Only some members of this committee are Jacobins. More are Sans-Culottes.
The National Guard
Made of up those who aren't at war in Austria (mainly former artisans or other tradesmen), this roughshod group forms the police force of the city, run by the Committee of General Security. They also answer to the Committee of Public Safety and here may lie some conflicts... Most of those in the National Guard are Sans-Culottes.