There was orginally only one Ordnance Survey for all of Great Britain and Ireland but now there are three. At the time of the partition of Ireland in the early 1900s, the original Ordnance Survey was split into three completely separate organisations:
OSGB is Great Britain's official mapping organisation, while OSNI is Northern Ireland's official mapping organisation. While all three organisations communicate and cooperate, they have some quite different approaches to the marketing of mapping and technical differences in their digital mapping formats, etc.. Ordnance Survey of Great Britain usually refer to themselves simply as "Ordnance Survey" (which is to some degree understandable as they are the biggest of the three organisations) but this can lead to confusion amongst mapping users. One major difference is that maps in Ireland (North and South) use the Irish Grid while GB use the National Grid. Such differences are important for example when mapping product and service providers wish to supply a UK-wide product as transformations of the data are then required.