A good writer is skilled in the technical art or crafting verse and prose.
An author is the person with the vision to craft a compelling story, an involving saga.
A person can be a great writer and a mediocre author. I’ve read many a novel that was perfect in technical terms, but dull as watching paint dry and unable to summon even one true emotion from the reader.
And I’ve read the polar opposite. The stories written with average skill that touched the hearts of millions.
You can always teach an author to be a better writer, but there are no guarantees that a skilled writer will ever be able to germinate the idea that can move mountains (of readers).
As any author can show you, the story comes first. If a great story comes to you, start writing, no matter your skill level. Get your great story out there.