A correspondent writes to ask: 'What is the difference between The window was broken with a brick and The window was broken by a brick.
Well, not much, from the window's point of view, or the house-owner's. And semantically, in this example, most people would hardly notice a difference. But they are grammatically different. What's happening is that two usually distinct constructions are overlapping because they are following a passive verb.
Grammars typically use such terminology as 'means' or 'instrument' for the first, and 'agent' for the second. Note that they answer different questions. The instrumental sentence focuses on the means used:
'What was the window broken with? or 'How was the window broken'. Answer can be: With a brick, or - so as not to repeat the with - A brick.
The agent sentence focuses on who or what performed the action:
'Who broke the window? or, in this case, 'What broke the window?' Answer cannot be With a brick. It has to be A brick - or, of course A brick broke the window.
With and without are the primary markers of instrumentality. But an instrumental meaning is often expressed by a by-phrase, and that's where the overlap with an agentive meaning comes in. You can check for instrumentality by seeing if you can substitute by means of, using, or some such phrase.
They communicated by signs.
They communicated by means of signs.
They communicated using signs.
They communicated with signs.
Note that you can't do this the other way round: an agentive meaning can't be expressed by a with phrase.
They were driven to town by a bus.
They were driven to town by a farmer.
*They were driven to town with a bus.
*They were driven to town with a farmer.
The only interpretation you could have for the latter is: 'along with a bus/farmer'.
There's a useful discussion of these constructions in The Cambridge Grammar of the English Language, pp. 673ff.