What is the difference between "optimizing" and "minimising"? When mathematicians speak of 'optimising' do they always mean 'minimising'?  Or does the term refer to a basket of techniques?
For example Wolfram MathWorld describes Optimization Theory as, "A branch of mathematics which encompasses many diverse areas of minimization and optimization".  
Is optimization synonymous with minimization?  Are all optimisation problems usually viewed in terms of minimising some cost or energy function?  If you read in a paper that some value is to be "optimised", do you assume the author means "minimized"?
For context if a paper refers to an rms (root mean square) value being "optimised", one would assume the idea is to minimise it.  

No, optimizing is about to find the best while minimizing is about to find the least. 
Now when minimizing a function $f$ on a set $D$ you want to find the $m\in D$ such that $f(m) \le f(x)$ for all $x\in D$ (in some cases you might settle for the value $f(m)$, but often you want to have the argument as well).
Now optimizing means that you want to find the "best" $m$ in $D$, but that relies on evaluating which element is better than the other. Often you describe this relation by assigning a "badness" to each element, that is a function $f$ such that $f(a) < f(b)$ means that $a$ is better than $b$. This would reduce the optimization problem to a minimization problem.
