It's fairly simple if you're talking about mechanical items: to break down = this is what the machine does. It is due to an internal fault. to be broken = this is what happens to the machine. The cause can be internal or external, so it is also possible for the machine to be the cause of its being broken. This is probably where your confusion lies.

I think they are effectively the same thing... I think Randy has it... Break down is generally used for bigger things whereas be broken is used for smaller things, but both can be used.

The expressions have the same meanings, but the verb "break down" is usually reserved for larger, complex things like cars, or even horses. The verb "break down" has some other meanings besides broken.

In my opinion, the difference between them is short enough, to use both of them with no worry :) Anyway, I have some sentences, FYI: "They had to break down the wall to get in": This is an active voice, an action to an object. Here, it is used as a verb. "broken heart, broken words, broken sleep, broken weather... " Here, it is in a passive voice, kind of "adjective". Hope it helps 'till there're better answers soon added.