The nouns count, number and numeral

The noun count often refers to the action or process of counting, but can also mean the quantity of something being counted or measured, as, for example, in the terms particle count or body count. A numeral is a symbol that denotes the result of a count—irrespective of what has been counted. The noun number often applies within either context. For example, the chemical term oxidation number can mean the numerical equivalent (formal charge count in an atom) of an oxidation state or the symbol, normally a Roman numeral, that expresses an oxidation state. Further, the word number is often used in an identifier contex, such as in the terms account number, social security number, and RTECS number (Registry of Toxic Effects of Chemical Substances number). Such identification numbers may include non-numerals and sometimes are composed completely from non-numerals (letters and punctuation marks).
The distinction between count and number can be important in avoiding ambiguities. In computer programming, it is a good practice to enhance program readability and testing by distinguishing between count and number variables, for example, by using prefixes cnt and n in variable names. A count variable dynamically counts something during program execution, where as a number variable holds an assigned numerical value.
The distinction between number and numeral is critical in separating an actual quantity from its notational representations. The same number can be expressed in different numeral systems—positional as well as nonpositional numeral systems [1].

References and Links
[1] Christopher Hollings: An Analysis of Nonpositional Numeral Systems. The Mathematical Intelligencer, Spring 2009, 31 (2), pp. 15-23.
[2] Karl Menninger: Number Words and Number Symbols - A Cultural History of Numbers.
[3] Encyclopedia Britannica/numeral system