Classically, I think that scripts are small/one-off bits that were written in an immediate language like Bash or maybe Python.

Scripts I think are meant to be run by tech people so might lack documentation, error checking, etc.

Often you'd write a script to set up the environment for a program; paths, environment variables, rotate previous logs and write PID files. Small scripts can evolve, and if they are part of an important program, can be more complex.

Programmers tend to write programs, while system admins used to write the bulk of scripts.

I'm not sure these divisions are as clear anymore, but that feels like how things originally evolved.