Learn English – Set off Vs Set out

What you call phrasal verbs have always been one of the messier parts of English syntax, and grammarians do not agree on what to call them, or how they are put together, or what to call their components.

Your first source is rather old-fashioned in one respect: it calls words like on and in ‘prepositions’ only when they take explicit objects; when they do not, it calls them ‘adverbs’. Other grammarians call on and in used in verb idioms like this ‘particles’ when they do not take objects; and still other grammarians, represented by your second source, claim that they are always ‘prepositions’, but may be used either transitively, when they take objects, or intransitively, when they don’t—just like transitive and intransitive verbs. This last version has the prestige of the highly admired Cambridge Grammar of the English Language (CGEL) behind it; but it is still contested.

Everybody, however, acknowledges that there are three different patterns, and my advice is that you focus on that. You will have to learn every single one of these idioms individually anyway, and will have to know which pattern each idiom follows. Don’t worry about what to call the pieces, just know how the pieces are used.

to shut something down simply means to make something nonoperational. When you shut your computer down, you bring it into a nonoperational state. If authorities shut a business down (by the way, another term that's used to refer to a company or business in English is operation), they legally close it down thereby making it nonoperational.

This idiom can also have a third meaning:

3 [transitive] informal to stop someone from doing something, especially to stop a player from having the freedom to move around or play well

So, to sum things up, in simple terms shut down just means to prevent something from keeping doing its thing by, possibly, liquidating it.

Example of a more colloquial usage:

He tried to ask her out, but she shut him down completely.

This is how this expression can be used in sports:

Our team will need to shut down their passing game if we are to succeed.