the +10C number (some designs use +5C) is used to be sure that anti-icing is switched on well ahead, to preclude intake icing.
The problem with two different manual temp call outs is that both were intended to make up for subjective judgement of crews deciding on whether to turn on the anti-ice based on visible conditions at their windscreen and wipers.
However having two dfferent temp recommendation between manuals only leads to more confusion among crews. Thus the intent was to go through all manuals among different aircraft and make them the same. I was assured by Boeing and Airbus that this had happened..