To be honest, I think that this is a fair comment. Accordingly, (and as this is a much debated article), I would like to propose this revised opening paragraph:
The terms Old Style (or O.S.) and New Style (or N.S.) are used in English language historical studies to indicate that the dating system used in the source material is one or other of the (historic) methods for determining the day on which the year starts. In the Old Style dating, the year began on 25 March, whereas in the New Style it began on 1 January.Death warrant of Charles I web page of the UK National Archives A demonstration of New Style meaning Julian calendar with a start of year adjustment. Additionally (more so in other parts of the world), the terms are used to indicate the change from the historic calendar [for example, the Julian calendar in Europe and the Americas] to the (modern) Gregorian calendar.The October (November) Revolution Britannica encyclopaedia, A demonstration of New Style meaning the Gregorian calendar.Stockton, J.R. Date Miscellany I: The Old and New Styles "The terms 'Old Style' and 'New Style' are now commonly used for both the 'Start of Year' and 'Leap Year' [(Gregorian calendar)] changes (England & Wales: both in 1752; Scotland: 1600, 1752). I believe that, properly and historically, the 'Styles' really refer only to the 'Start of Year' change (from March 25th to January 1); and that the 'Leap Year'  change should be described as the change from Julian to Gregorian."Spathaky, Mike Old Style New Style dates and the change to the Gregorian calendar. "increasingly parish registers, in addition to a new year heading after 24th March showing, for example '1733', had another heading at the end of the following December indicating '1733/4'. This showed where the New Style 1734 started even though the Old Style 1733 continued until 24th March. .. We as historians have no excuse for creating ambiguity and must keep to the notation described above in one of its forms. It is no good writing simply 20th January 1745, for a reader is left wondering whether we have used the Old or the New Style reckoning. The date should either be written 20th January 1745 O.S. (if indeed it was Old Style) or as 20th January 1745/6. The hyphen (1745-6) is best avoided as it can be interpreted as indicating a period of time."

 References are unchanged from current version
Comments?