Earlier today I listened to a presentation about short story writing. One of the two presenters--an established mystery short story writer--claimed that professional publications pay by the word and that publications that pay flat rates are not professional publications.
What a crock.
I've sold short stories--some of them mysteries--to many publications that pay flat rates The flat rates some of these publications pay exceed the per-word rates that the top mystery magazines pay for stories of equivalent length. And sales to some of these publications were used to qualify me for active membership in the Horror Writers Association, Mystery Writers of America, and Science Fiction and Fantasy Writers of America.
So, whether a publication pays per-word or pays a flat rate for its fiction is not, in and of itself, an indication of whether or not the publication is a professional market.