I suppose everyone has their own way of defining these things, and some people get more determined about it than others, and some even strident. You’ll have your own opinions, and that’s fine, I’m just giving these the way I see it so you’ll understand my next three Friday posts. If you want to disagree in the comments, go ahead, I’m not going to argue with you.
So, in alphabetical order:
Anthology – a group of stories by different authors, edited, often with a specific theme, time period, or intent to group the stories cohesively. Example: The Hard-Boiled Veldt: Murder at the Water Hole, edited by Flinky Flanders.
Collection – a group of stories by a single author, edited by that author or another person. Could be a “best of”, several early or current works, something themed, or a “complete” set. Example: The Complete Stories of Flinky Flanders.
Omnibus – a group of two or more novels or other long works by a single author or by authors connected by subject, theme or time. Example: Three Early Novels of Flinky Flanders.
So that’s it, simple enough, works for me. For the next three Fridays I’ll be posting one of each.
Tip the Wink 
I’m absolutely in agreement with your definitions — they’re the ones we used in The Encyclopedia of Science Fiction and The Encyclopedia of Fantasy after all! — although, since those halcyon days, the occasional book has joggled the boundaries. As example, I’d suggest that The Private Life of Elder Things by Adrian Tchaikovsky, Adam Gauntlett and Keris McDonald is a collection rather than an anthology despite there being three authors involved, in that the three quite clearly collaborated to produce a set of related stories. There have been other cases (none of which, of course, I can remember right now) where two authors have engaged in a similar exercise.
And, as a special case of novels-bound-together book, you have the dos-à-dos/tête-bêche books produced by the likes of Ace in their Ace Doubles; I don’t think you could reasonably call these an omnibus, yet clearly they’re not a collection/anthology either.
I know, I should have shut up several paragraphs ago.
John, thanks for the insights. You’re right, not sure what I’d call and Ace Double, but novel collection comes close, and in a punish way.
Works for me, too, Rick.
Thanks. Are you going to NO?
I’m a big Flinky Flanders fan, too!
Flinky is a brilliant writer and editor, yet so few are familiar with his work.
Flinky is the man (or woman, as the case may be)!
The definitions? I’d say you nailed it.
“Flinky is the man (or woman, as the case may be)!” Absolutely
A good way of describing it. I agree.
Thanks, Charles.
The Brits would seem to have a problem with your sensible definition of omnibus. Two on my shelves: The Dr. Thorndyke Omnibus (R. Austin Freeman) – a collection by your rules; and The Omnibus of Crime (Dorothy Sayers, ed.) – an anthology per RR. Still wonderful books, whatever you call them.
Yes, and they aren’t the only ones. When it comes to “omnibus”, some editors like to also use it to indicate a Very Large or Very Significant collection, which would allow, because it includes works from more than one previous published collection, the Thorndyke.
The Sayers edited Omnibus of Crime, like the Omnibus of Science Fiction edited by Groff Conklin which I have, and others, just use the word to indicate volume. In my opinion these two are mistitled, and are in fact an anthology, plain and simple.
Also note I point out these are my definitions, as opposed to rules and thus are not immutable.