The generically distinct lecture titles for Oscar Wilde's American tour are:
—The English Renaissance and The Decorative Arts, continuum (see The Decorative Arts)
—The House Beautiful
—Irish Poets and Poetry of the Nineteenth Century (given once in San Francisco)
—The Relation of Art to Other Studies (a specially prepared talk given once in Hamilton, ON)
Ross's text is a collation of reports, manuscripts, and typescripts of the lecture in its early iterations.
Wilde amended the content with successive lectures so that by the time he delivered it for the final time in Buffalo it was 'quite different', and 'the final text is closer to The Decorative Arts. 
The English Renaissance had been 'too lengthy and theoretical for many in Wilde's audience'  so he shortened and retitled it to give it wider appeal. The lecture was redrafted in early February as 'The Decorative Arts', and Wilde continued to domesticate the content as the theme evolved. As such, the evolution of these two lectures can be seen as a continuum with the most conscious transition occurring in Chicago on February 13, 1882 .
Not a title that Wilde ever used. It was a name given by Ross to part of this early version of the lecture.
During the early weeks of the new lecture, Wilde was occasionally billed as still lecturing on The English Renaissance causing Wilde to write to his manager to ensure that it was his new lecture being advertised.
This may have ended the confusion for his audiences, but not for historians, as the new lectures in turn were variously titled and reported; also 'it is probable that Wilde adapted them slightly to suit different audiences'. 
A definitive version 'was complete'  by the time Wilde lectured in San Antonio on June 21, 1882.
On May 11, 1882 Wilde gave the lecture on a return visit to New York. Even by this time the content had changed such that it was 'almost a different lecture'  from The Decorative Arts I.
What Wilde said that night was transcribed the next day in the New-York Tribune, ostensibly verbatim, in an article headed:
The Tribune transcription is important as it was later reprinted, most notably in two books which are now in the public domain and thus appearing legion online. Unsurprisingly these reprintings were given different titles, despite, being the same text of this later, but still evolving lecture 'The Decorative Arts'.
Wilde created this alternative talk for when he lectured more than once in the same city. It was first required on his return visit to Chicago on March 11, 1882.
The lecture was a domesticated version of his general theme that focused on the beauty of handicrafts in the home such as in furniture, carving, and wallpaper.
The lecture became known as The House Beautiful but it began life as 'Interior and Exterior House Decoration or, confusingly, Art Decoration, often with a longer more descriptive subtitle, such as in Philadelphia on May 10, 1882.
A specially prepared talk given to a girls' college on May 31, 1882 in Hamilton, oN .
A standalone lecture not directly descended from other lectures.
In essence this was a distinct lecture, although Wilde had tended towards the subject of dress when apropos in previous lectures (a thesis explored in Oscar Wilde On Dress).
Wilde later (1885) published a full version of this lecture for an American audience in an essay that has recently been discovered. See: The Philosophy of Dress.
Outwardly this was a continuation of the US lecture as 'sections are repeated in very similar ways'; nevertheless, 'the majority of the lecture had been revised.' 
and various others.
For a definitive review of the UK/Ireland lectures see Geoff Dibb, Oscar Wilde, A Vagabond with a Mission, The Oscar Wilde Society, 2013
Glaenzer: Decorative Art in America: A Lecture (1906)
* Miscellanies: Vol. XIV of The Complete Works of Oscar Wilde, 1908, fourteen vols. edited by Robert Ross.
 O'Brien, Kevin. Oscar Wilde in Canada: An Apostle for the Arts, 1982.
 Holland, Merlin. The Complete Letters of Oscar Wilde edited by and Rupert Hart-Davis, London: Fourth Estate; New York: Henry Holt, 2000.
 Dibb, Geoff. Oscar Wilde, A Vagabond with a Mission, The Oscar Wilde Society, 2013.