Is there a difference between a range and an interval?

Question

Can the terms 'interval' and 'range' be used interchangeably or do they describe different things?

I am talking specifically about sets of numbers under a suitable $<$ relation, such that they can be described as $r = [a,b]$, $(a,b)$, $[a,b)$, or $(a,b]$, meaning that for any $a < c < b$, we have $c \in r$ (and $a$ and $b$ depending on the respective brace used).

Answer 1

Your sets above are called intervals. "Range" is unusual .

Answer 2

Can be. But convention gives clarity by usage/familiarity.

If $y=f(x),$ then you can consider an interval anywhere in the full extent of domain of independent variable $x$. Range is used for difference of max/min of dependent variable $y.$