I think the origins of the term 'script' in this context, come from shell scripts, and jcl scripts, where mostly, the interpreter only provided flow control, and the meat of the task was sub-tasked to specialist processes. Eg. sort, split, find xargs, gzip etc. As such the control files (source code) used by these types of interpreters were likened to the scripts used to give actors directions in theatre and movies.

Whilst Perl can still be used this way for simple tasks, by bringing the functions of many of the separate sub-task procesess 'in-house', and combining them with composable data structures, and a rich set of built-in functions to manipulate them; and modular sources; Perl became a fully fledged, very high level, programming language. So, the distinction between scripts and programs breaks down.