The UP were seperate from the Conservative Party - indeed, the merger between the two was the reason that the Tories in Scotland are called The Scottish Conservative and Union Party.
They were almost identical to the Ulster Unionist Parties - the DUP and the UUP took the Tory whip until 1973 - the UP did throughout their existence.
Had the Tories won 14 more seats in the last election, the ruling coalition just now would be the Tories and the DUP not the Tories and the LDs. This would be a coalition not the "same party".
There's a reason they were seperate from the Conservatives and that's because, politically, during the 20th century Scotland was a lot more liberal than England and the use of the word Conservative wasn't seen as positive as elsewhere.
There were, of course, more pecularly Scottish reasons that they remained a seperate party.
The Conservatives weren't the "small government, free market" party people think of them now - and the Unionist Party's membership weren't signed up to the idea of them being the traditional opponents of the Whigs (for religious reasons).
Granted, someone who would vote Conservative in Scotland at the time would've voted UP but then, someone in Northern Ireland who would vote Tory would vote DUP.
I was reading an old school text book I've kept after watching some WWI stuff last night

<thief> and it mentioned that there was a split in the UP after Irish Home Rule - believe it or not, part of that split ended up forming the Scottish Party who merged with another party to become...
...the SNP
So, it could be claimed that the natural successor of the Unionist Party is as much the SNP as it is the Conservatives.