I personally define mistakes as "faults". By this I mean that if a child has understanding of the maths subject in question, he or she should be able to do the question correctly. Thus, the mistake can be attributed to things such as sloppiness, inattentiveness, and so on.

On the other hand, errors, deviations from the correct answer, can happen for other reasons. Intuition, for one. A specific example is how humans perceive numbers logarithmically, that is, larger numbers spaced closer together. (eg: "million" and "billion" are both very large, but to the brain there is little difference).