No, Companies House has just one website. It is used for company formations for the whole of the UK, but they have a separate registrar’s office in each of the UK’s three jurisdictions - England and Wales (Cardiff office), Scotland (Edinburgh office), and Northern Ireland (Belfast office). There is also an information office in London.
If you wish to register a limited by shares company in Scotland, you simply need to complete form IN01 on the Company's House website. It will be processed by the Edinburgh registrar. Alternatively, you can set up a limited company in Scotland through any online company formation agent in the UK.