@boomerang,
Math calculating is basic straight forward math calculations - like addition, subtraction, multiplication, division, various equations. The problem would be presented as 2 + 3 = ?
Reasoning is more the word problems - so you have to reason out what you are trying to calculate. Jane had two cats, bob has three cats, how many cats do they have in total?
Same answer, basically same problem, but you need to figure out in the second what you are trying to calculate.
My daughter has participated in the math olympics before - they divide into math calculation or math reasoning. She stinks at math reasoning, but does very well in calcuation.