The term Unionist historically meant a supporter of the Union between Great Britain and Ireland, and it was for instance in this sense that the Tories for many years called themselves the Unionist Party.
The word has gradually changed its meaning, however, and it now tends to mean a supporter of the Union between England, Wales, Scotland and Northern Ireland, so the independence battle in Scotland is now between Nationalists and Unionists.
For instance, the well-kent commentator Iain MacWhirter wrote this recently: “The danger now for the Unionists is that Mr Salmond – following the lead set by Mr Darling and Mr Cameron – may offer a version of independence that is so close to devolution max that Scots vote for it out of spite at not seeing their favoured option on the ballot paper.”
I’m not really aware of a better word – from a Scottish perspective, I guess one could talk about a Britainist or a Great-Britainist, but I think that might be a hindrance to understanding rather than a help.
The shift in meaning is also not really a problem from a current perspective, but it does occasionally lead to confusion when modern readers are confronted with older texts containing the word ‘unionist’.
I tried to do a plot using Google Ngram Viewer, but I have a feeling the figures are probably dominated by Irish Unionism. Does anybody have access to a Scottish corpus?