Interpolation refers to expansion of expressions into another value. I tend to use this and “expansion” somewhat interchangeably, but here the thinking is that expansion is often the implicit result of evaluation whereas interpolation is more specifically the expansion within another value (typically to produce a string).
Expansion in bash is generally done using $ with
specific variations depending on the type of value. $(...)
is used for subshell epansion suitable for general expressions and ${...} is used for
variable expansion. For variable expansion the braces are typically
optional but I use them consistently.
In bash the interpolation syntax is necessary anytime the value of variable is desired (likely as a consequence of its use as a shell).