Q:

Differences between variable and variate

From Wikipedia

A random variate is a particular outcome of a random variable.

If I understand correctly, a random variable is a measurable mapping, and a random variate is just a member of the codomain of a random variable.
In general, what differences are between variable and variate in mathematics? What do they mean respectively?
Thanks!

A:

A random variable or stochastic variable is a variable whose value is subject to variations due to chance (from Wiki). 
A random variate is a particular outcome of a random variable: the random variates which are other outcomes of the same random variable would have different values (also from Wiki).
Suppose $X$ is a random variable which stands for the outcome of tossing a fair dice. So $X$ can take value from $1$ through $6$ with equal probability of $1/6$. Now you actually toss a dice and get a number $4$. This number is a particular outcome of $X$, and thus a random variate. If you toss again, you may get another different value.

