Green = Inexperienced, needs some miles in whatever the horse is doing. Same goes for riders. Example: I'm a pretty experienced rider, but a green jumper. The green label can carry over to different stages, I like to think of it like a modifier of another label.
Started = What I would call "saddle broke," basically knows how to carry and take direction from a rider, ready to start putting miles under. Takes a highly experienced and competent rider. Also Green Broke.
Broke = Fairly easily manageable. Knows forward, backward, left and right, W/T/C, and whoa. Has some experience and miles, and easily handles common "spookies" (tarps, ground poles, flags, ropes, etc.) Maybe ready to tackle a light show, but still has "kinks." Needs some fine tuning. Experienced to confident intermediate rider. I would say that my current horse falls in the early stages of the Broke designation.
Well Broke = In addition to "Broke" skills, horse can collect and do some of the more discipline specific movements. In a perfect world, the well broke horse is bombproof or near to it. Beginner rider can easily handle, and a more experienced rider may get a lot from this horse.
Finished = This horse is well educated, generally push button. Most riders can get a lot from this horse if they know what and how to ask. This horse is also likely to be fairly competitive at shows in whatever discipline he is trained for. IMHO, there are relatively few truly finished horses out there, especially compared to the number of horses who fall into various stages of "Broke." Finished is a discipline-specific state of training.
A stubborn horse walks behind you, an impatient one in front of you, but a noble companion walks beside you ~ Unknown