Killer Clown or Clown Killer?

Hi guys, I need some help toward these two words.
I am waiting for AHS Freakshow and there is a clown character that people write on websites "Clown Killer", my question regarding this is:
Why to use Clown Killer instead of Killer Clown?
Hope anyone helps!
MENSAGEM PATROCINADA Para aprender mais sobre os Tempos Verbais baixe agora o: Guia Grátis de Tempos Verbais em Inglês. Ele contém um resumo bem estruturado para revisar os conceitos que você aprendeu na escola.

Clique aqui e saiba como baixar!
Hi !

It depends on the way you want to build the sentence.

Clown Killer: Palhaço Assassino ou seja O Palhaço seria o sujeito e o Assasino o adjetivo para o Palhaço.
Killer Clown: Assassino Palhaço ou seja O Assassino é o sujeito e O Palhaço é o adjetivo para o Assassino.

The meaning changes a little but it depends on what is the main.

Avatar do usuário PPAULO 39755 6 32 695
You are not alone, certainly you are in good company (many people get puzzled with that one). ... ar%20I.pdf

7. Noun Strings
In English, an adjective is supposed to modify a noun. But there are not enough adjectives
to go around so a noun is often used in its place. Don’t overuse this construction since
meaning can be obscured; often a prepositional phrase is better.

Example: “woman killer” can mean a killer of women or a female killer
“nutrition facts” Here the meaning is clear but use of an adjective or a phrase
sounds more like English: nutritional facts, facts about nutrition
“customer service representative” If you really need such a rank construction, you
should put a hyphen between “customer” and “service” since the words used
together are a noun, here masquerading as an adjective.

Well, it goes with context. In this special case it´s already a fixed expression of sorts (an urban legend) and then by the infamous clown that was a killer (murderer), John Wayne Gacy.

In fact, "the clown killer" could be misunderstood as a guy that kills clowns. As you see in the above explanation.
And "clown killer" as a random way to refer to any "clown killer" (as per above definition).