You could think of a script to being the same as a dos
batch file...If you consider a dos batch file to be a
program, then the same distinction could be made about
linux script. Generally a script calls other programs
like "cd" or "cp" or whatever. A program, if you
think of a program written in C++ or something uses
lower level, built-in functions.

A script is a program but a program isn't necessarily a script.

The general consensus is that a script is a program in an interpreted
language such as bash, Perl, PHP, Tcl/Tkl, Python or whatever. A program can
also be written in a compiled language such as C, C++ or Pascal, or it can
be written in assembler, but in this case it is no longer a script.

what is the interpreted language?

There are 2 main families of language.

There are those which read your source code and interpret what you want to
do *while* reading through your script, hence the name "interpreter".

Then there are those which take your source code and convert it into
something which your processor and operating system understand without
having to use an interpreter. Since these programs are converted into
binary, or "compiled", they run much faster than interpreted programs.