"The Guardian" changes to "The Observer" on Sundays, "The Sun" used to become "News of the World". Most (if not all) British newspapers do this. The names often reflect the fact that they are the same newspaper (e.g. the "Daily Mail" becoming "The Mail on Sunday").
Essentially they are the same newspapers, so why do they take different names? Sure, they have different staff and different features, but so do the Saturday editions of papers, and those keep the name of their weekday counterpart.
How did this tradition arise?
The papers you are discussing are in fact traditionally separate, sister, titles, which have long histories and were for much of their lives independent of each other.
Thus the Observer was founded in 1791, well before the Guardian (1821), and although both shared a worldview in the past century, in that they were left-of-centre broadsheet titles with a predominantly middle class readership, they were only combined in the same group in 1993. Similarly, the News of the World had a history as an independent family-owned weekly newspaper that dated back to 1843. The paper had run into serious financial difficulties by 1968, when it became the first British newspaper purchased by Rupert Murdoch. Murdoch used this toe-hold to go on and acquire the much-younger daily Sun (est. 1964) a year later, and though both also shared a focus in the period since his takeover, in that they were right-of-centre tabloid titles with a predominantly working-class audience and a significant focus on celebrity news and scandal, he ran the two papers independently until the NoW was shut down in 2011 after becoming fatally (in terms of its popularity) caught up in a rather horrible phone-tapping scandal, which I can't really enlarge upon owing to the 20 year rule in operation here. All these titles had separate existences and completely separate editorial staffs – so it's not a case of a daily paper "turning into" a Sunday one, as you assume. Nor did the Saturday editions of the Sun or the Guardian have their own staffs; these editions were put out by the weekday staffs of the two dailies.
The reasons for combining daily and Sunday titles in the same group typically have to do with industrial economies of scale – for example in paper buying, though Sunday papers also made use of presses that would otherwise be lying idle one day a week – while the tradition of maintaining different staffs, and running Sunday and daily papers independently (which has long been the standard in the UK even when the two titles are under the same ownership – as has been the case with The Times (est. 1785) and the Sunday Times (est.1821) since 1966, and was also the case when The Independent (est. 1986) launched the Independent on Sunday (est. 1990)) – have to do with their different functions and, to a lesser extent, audiences.
Sunday newspapers have, at least since the 1960s, focused on longer-term and investigative stories that are less dependent on the daily news cycle – the Sunday Times was noted for decades for its investigative "Insight" team, which uncovered stories such as the thalidomide scandal, worked on lengthy exposes of the Soviet spy Kim Philby and was behind the 1994 "cash for questions" investigation which revealed that some Members of Parliament were willing to take money from lobbyists to ask questions in the House of Commons. The News of the World, similarly, specialised in off-diary celebrity scandals. In addition, Sunday papers boost their viability by capitalising on the demand for reporting of Saturday sports fixtures and – in common with the Sunday editions of US daily newspapers – by running numerous weekly "ad-get" supplements covering everything from property to book reviews. This requires them to have a more extensive team of specialists and overall a differently-balanced staff than a daily paper does.
Typically, as Stephen Glover (who was founder editor of the Independent on Sunday) describes in some detail in his book on the two Independent titles, there is actually considerable friction between the editors of sister daily and Sunday titles as they compete for resources, and the Sunday editor may come under some threat of losing his or her independence from time to time as well. Much the same often applied to the staffs. Horrie and Chippindale describe attempts by the notoriously aggressive journalists who worked on The Sun to hack the computer systems at the News of the World (located in another office in the same complex) to find out what stories their supposed colleagues were working on.
In recent years – again I am at least partially constrained by the 20 year rule – the financial viability of UK Sunday-only newspapers has become increasingly tenuous, but this problem in fact dates back some time, certainly to the late 1980s and early 1990s, when the Observer became unprofitable and the solus upscale Sunday Correspondent and far-left News on Sunday both launched and rapidly failed. In this recent period, most newspaper groups have considered, and to various extents attempted to implement, combined editorial teams and "seven-day" news operations. Murdoch's decision not to relaunch the News of the World or replace it with another standalone Sunday paper, but to begin publishing the Sun on Sunday (2012), with one editorial team working across the two titles, needs to be read in this context.
Sources
Stephen Glover, Paper Dreams: The Story of the Independent and the Independent on Sunday (1993)
Chris Horrie and Peter Chippindale, Stick It Up Your Punter! The Rise and Fall of the Sun (1990)
Chris Horrie and Peter Chippindale, Disaster! The Rise and Fall of News on Sunday (1988)
In addition – and I think this evades the rule here against "personal anecdote" – I helped to cover the British media industry as a reporter for UK Press Gazette from 1990-1993.