I don't think I fully understand ESC's, not sure if anyone really does, but if they do could they take a minute and help me out.

I am getting a plane, which calls for a 35A Airboss ESC, well they are horribly overpriced and I am looking at Thunder power ESCs...

My question is does the ESC have to be able to handle a burst from battery. (i.e. If battery says burst of 40C and my ESC says it can handle 35 on burst.) Would the ESC break down and would I see my beautiful bird fall like a rock from this example I gave?

Now, if the plane calls for a 35A Airboss then it should be able to use a 40A Thunder power one right, and if it is too big of an ESC am I wasting battery power?

I am horribly confused,

Thanks in advance for any information you guys give.