According to A Note on the Text in my venerable Penguin paperback, Melville's agreement with Bentley was that "the English edition was to appear at least a fortnight before the American." Melville would receive £150 on delivery of the manuscript as an advance of 50% share of the profits. (Using the "pounds" version of Lemuel's "purchasing power calculator," that's equivalent to a wage today of £116,000, or $183,103.)
The text was heavily edited to remove "dubious sexual, or political, or religious overtones" (Penguin). Chapter 25 was entirely missing. Most confusing to critical readers was the absence of the Epilogue—if everyone perished at the end, then who's telling the story?
Contrary to prevailing myth, the initial reviews were not uniformly scathing. They ranged from "...a most extraordinary work..." to "...wantonly eccentric; outrageously bombastic..." This collection of contemporaneous reviews is worth reading.
The American edition was published by Harper & Brothers, New York, "probably on November 14, 1851" (Hershel Parker). The title on this edition was changed to Moby-Dick. It was published as a single volume in a run of 2,915 copies.
Thus the novel was typeset twice, which resulted in two versions of the text (the English version unsympathetically edited to boot). The dedicated sleuthing of Harrison Hayford and Hershel Parker, later with G. Thomas Tanselle, rationalized the differences in the two versions to determine "as nearly as possible the author's intentions." The result was the Norton Critical Edition (1967), followed by the Northwestern-Newberry edition (1988).
The logic whereby Hayford and Parker untangled the M-D knot is for another post. Of course, not everyone agrees with their editorial choices, so the search for Melville's "intentions" continues (see the Longman Critical Edition). Some publishers skirt the issue entirely by simply selling (error-ridden) public-domain versions.