First, "arithmetic" and "count" have different syntactical functions. "count" can be used as a verb, but "arithmetic" can NEVER be. Since you want to compare them, then you shall compare them when they are used as a "noun".
"Arithmetic" only refers to the operation of plus, minus, multiplication, and division. It is part of mathematics subjects.
"count" is an action of counting or a total obtained by counting. Hence, generally speaking, "count" only use the function of "addition". However, such an addition function is only limited to a certain increment, for example, count by one, five or ten ...
Hence, even though they both can mean "calculation" (計算), but they do have fundamental difference from the way they calculate.
2013-06-20 21:44:13 補充：
syntactical function = 詞性
2013-06-24 01:59:31 補充：
Generally speaking, YES!