Why some sources put the definite article, some sources put the indefinite article and other sources doesn't put anything before this phrase "Key to [something specific or something in general]". It's a matter of style /BA and AE differences or what?
It can be a straightforward noun used in a metaphorical way: this thing is the key (that opens the door) to success. Or it can be more adjectival, meaning "very important, essential", and in this sense it doesn't have to be unique: the key factors in success are luck and money; hard work is key to success; bribing the police is also a key ingredient.
There's no particular style difference; the word just has two kinds of use which happen to come very close together sometimes.
Entangledbank explained it pretty well. Either one is technically correct: "the key to success" (where "key" is a noun within an idiomatic expression) and "key to success" (where "key" is an adjective). However, "the key to success" is the more common idiom. Still, as we both stated, either one is correct.