The difference between the terms "anthology," "collection" and "omnibus"
ANTHOLOGY (noun) : a book or other collection of selected writings by various writers usually in the same literary form, of the same period, or on the same subject. e.g. a book of poetry by various poets or a book of several short stories all written by different authors.
Now, when you publish and anthology of short stories or poems by various authors, it is acceptable to use the term "collection" in the title rather than "anthology," but the book should be categorized as an anthology. An anthology is a collection, but a collection is not always an anthology.
COLLECTION (noun) : a book of selected writings from various books or a selection of short stories or poems by one author of the same theme or various themes. e.g. a book of short Christmas stories all written by the same author.
Although it is done frequently. using the term "anthology" in a title for a collection of stories or poems from ONE author, is actually not supposed to be done. The title (if it includes such information) should use the term "collection" to describe the contents of the book.
OMNIBUS (noun) : a volume of reprinted works of a single author or of works related in interest or theme. An omnibus contains several complete books by one author.
e.g. a book of supernatural stories by Terry Pratchett. A complete content of each book is used.
It is rare to see an omnibus with anything other than omnibus in the title, which is as it should be.