Rightio: for a Text Response Essay you're expected to deal with the text in a lot of detail. Every paragraph you write MUST be about some part of the text. You're allowed to include some background information about the author's life and times, but only a couple of sentences, and only if it's relevant to the discussion.
For context, however, the text is just a 'springboard,' meaning it's only the beginning of your ideas. Although your essay has to build on the ideas in the text (and you should mention it explicitly at least once; this is not an official criterion, but VCAA can penalise you for it anyway, trust me
) After that, you can use whatever you want: external sources like news stories & current affairs, historical events, famous people, books, songs, quotes, other literature etc. etc. Not every paragraph has to mention the text, you're only using it to say something about the Context/prompt.
I guess an easy way to differentiate the two would be that for Text Response you use the prompt to discuss the text, whereas for Context you use the text to discuss the prompt.
It's annoyingly similar (esp. for expository style Contest pieces) but here's hoping VCAA lift their game for next year's Study Design.
Not much consolation at the moment, sorry