200 kilometers is 125 miles ... a little more than a 100 mile century, but not an outrageous length. Note, however, that the extra 25 miles is usually at the end.
A brevet is a timed event, with time cuts for intermediate "control" points as well as the ride finish. You do not have to be very fast to finish within the time cut (13.5 hours for 200km), but you need to keep going at a modest pace. Elapsed time, rather than time in the saddle, is what counts ... so those food stops are on the clock.
On a supported century, volunteers provide you with food and drink at intermediate points along the ride. On a brevet, you stop at markets. Typically you buy food and get your brevet card signed at the same stop. Remember, you're on the clock, so don't dally too long unless you're a fast rider.
In addition to food stops, century ride support typically includes a sag wagon. Occasionally a brevet may feature support at a remote intermediate point where markets are not available, but usually you are on your own, and sag support is unknown. In fact, there is a rule against receiving help from a person other than rider on the same brevet, except at designated control points.
You get a cue sheet for your century ride, and you get a cue sheet for your brevet ... so far so similar. But the supported century ride probably features road markings or even volunteers pointing the way. The brevet route is not specially marked ... you'll have to read the cue sheet and navigate.
The fee for a century ride covers a variety of support expenses, such as the sag wagons and food stops, and often includes a portion for charity and advocacy work of the sponsoring club. The fee for a brevet is usually much less, covering insurance and the minimal support provided, typically including a snack at ride end. A typical fee for a 200km brevet might be $15 or even less. Longer brevets, especially with overnight stops, may cost more.
Supported centuries typically take place entirely in daylight hours. A 200km brevet may take place entirely in daylight in the summer, but most brevets either start before dawn or extend beyond sunset (and some even start in the evening). Whenever a brevet is not entirely within daylight hours, a randonneur is required to have adequate lighting and reflective gear, as spelled out in article 10 of the Rules for Riders. Note in particular that lights must be attached to the vehicle (the bicycle); lights attached to the rider are not sufficient.
Supported centuries are nominally "rain or shine", but in practice centuries are scheduled in periods where "shine" is a reasonable expectation. The brevet season starts earlier in the year, and often extends further into fall. Randonneurs in the northwest are accustomed to riding long distances in the rain.
The bicycle you use for a supported century will also work for a 200km brevet, provided you have lights if the ride will take place partly in low light or darkness. However, you'll notice that a lot of randonneurs are riding bicycles with fenders, generator lights, and front or back racks. You'll see a lot of handlebar bags, which serve both to hold the cue sheet and to feed the randonneur between controls. Many randonneur bicycles will sport fatter tires than racing bicycles, and randonneurs will be wearing shoes that make walking practical.