There seems to be some mystery about shell scripts, that they are somehow not related to what we can do with an interactive shell. In fact, nothing could be further from the truth. Most of the power of shell scripts derives from all the utility programs available. Which is exactly the same case as happens with an interactive shell. The only difference, is that shell scripts employ some sort of automated logical test and looping construction, whereas most users do these operations with their head.
One of the big uses of shell scripts, is to ``fix'' some particular set of commands. If you find yourself typing the same series of commands in, over and over again, it may be time to learn how to embody this set of commands in a shell script.
All (major) shells have a scripting language. Not all of these scripting languages are equally powerful. Most scripts are probably written in the original Bourne shell. But the Korn and Bourne Again shells are powerful to allow the writing of such things as BASIC interpreters.