You haven't used too many different brake / break spellings - both have been used at different times to describe the same vehicle.
In the olden days, yes, a brake coach or more commonly brake van was situated at the back of (especially) a goods train. There was no continuous braking on goods wagons, and the brake van was equipped with a wheel handbrake. The guard was therefore able to stop his bit of the train should a break in coupling occur. For this reason, the term "break van" was used in English railways until the 1870, when "Brake van" took over. The van was usually heavily ballasted to add to the braking power. Initially, they were open, then had a hut built to protect the guard from the elements, but with a veranda, to aid visibility.
The guard was not there just to act in the event of a break. He was active in applying the brake on downward gradients and when slowing to stop, to add additional braking effort to what was fitted to the locomotive - Victorian brakes were less than superb, and every little helped. Considerable route learning was needed for the brakeman or guard. As well as brake vans, there were also passenger brake carriages, having both passenger accommodation and a separate bit at the back, equipped with a wheel handbrake, for the guard. This was mainly for use in emergency, or if the rake of carriages was parked without a loco.
The big move away began post-Beeching. Modern diesel locos and new rolling stock allowed for continuous or part-continuous vaccuum braking. Fully fitted goods trains were no longer required to end with a brake van, and the guard could now sit in the rearmost driving cab, as a sort of safety supervisor. By 1985, there was agreement that most goods trains did not need a guard, but anything hazardous still ended with a brake van until around 1990. You can still see them on heritage railways, such as the
East Somerset.