Batch size is amount you're shooting for into the fermentor.
Boil Size is the amount pre-boil, that is, your batch size plus whatever is lost as steam during the boil.
Not really related to efficiency. Efficiency has to do with the amount of sugar you extract from the grain during an All Grain Mash and Lauter.
If you leave too much wort behind in the kettle, that will skew your efficiency numbers, but not really effect efficiency.