The Irish and Scottish varieties of the Goidelic language family have far less mutual intelligibility than the English and Scottish varieties of English. Scottish English forms a pretty smooth continuum between "English with a Scottish accent", and what you'd call "Scots" or "Lallans".

But Scottish Gaelic is the tongue that gets the downgrade to "Gaelic", despite it being simply called Scottish for the vast majority of Scotland's history. Despite it literally being the reason for the country's name.

Scottish English was literally only called "Scottis" instead of "Inglis" as the Lowlanders gained a greater sense of national identity and distinctiveness from the English further south. At that point, funnily enough, the Goidelic spoken in Scotland ceased to be called "Scottis", and became "Erse" instead.

It is quite impossible to separate this insistence on distinguishing "Scots" from English, from suppressive efforts towards the indigenous Gaelic language of Scotland. You can see the exact same dynamic in Northern Ireland, where unionists play up the supposed variety of "Scots" spoken by the Ulster planters and their descendants as a fully distinctive language equal to Irish, as a means to delegitimize Irish as the primary indigenous language of the land.

I don't say all of this from a place of antipathy towards the speakers of "Scots". One need only read some Burns to see that the variety of English spoken in Scotland diverged heavily from the varieties spoken further south, and that diversity is beautiful. But the label is politically charged, and fundamentally it is a weapon - and always has been - pointed in the direction of Gaelic-speakers.