As in, unlike the USA or Switzerland where a number of largely autonomous entities banded together and created a nation together, we go from being a unitary nation with little or no regional autonomy, to a newly federal one where the states/regions/provinces/home countries/whatever get more and more autonomy. Of course, Scotland was independent before, but that was four centuries ago.
So since 1999 if I recall correctly, Scotland has its own legislature and its own government led by a "First Minister" (as opposed to the Prime Minister in London), but in the beginning with very limited powers and responsibilities. Those have been increasing over time, with the same thing happening - but at different speeds - in other parts of the UK like Northern Ireland and Wales. By now, I would argue that the differences between Scotland and England or Wales are bigger in some ways than the differences between US states - one of the obvious differences is that in Scotland, higher education at public universities is free for all Scottish students, while in the rest of the UK the tuition fees have increased considerably in recent years.
A year or two ago when this referendum was being debated, the UK government had to decide between a referendum with two options (independent or not), or one with three options (independent, maximized powers for the Scottish parliament within the UK, or the status quo). At the time, they figured they were being smart by picking the two-option referendum, as they didn't think the proponents of independence would ever really stand a chance, leaving them with their hands free after the referendum, whereas in a three-option referendum the victory for the so-called "devolution max" would be almost inevitable. Ironically, with things coming down to the wire as they are, they are now essentially offering this devolution max of their own volition, in a desperate bid to avoid a victory for the full independence camp.
Neither, honestly. The UK is quite complicated. Even the thought experiment of a USA with only four states doesn't really work, among other reasons because the biggest "state" by far, England, doesn't have any parliament or executive of its own - the "federal" parliament, including the Scots, Northern Irish and Welsh Members of Parliament, governs England. Which of late has caused some resentment among the English - that the Scots and the others get to vote even on issues only affecting the English, while demanding more and more autonomy on their own affairs. But it will still take a long time, if ever, before the English demand and get their own parliament, I think - because of the signal it would send to the rest of the UK.
An easier comparison might be to the Quebec independence referendum back in 1995, if you followed that a bit - a small, culturally and historically separate part of the bigger country, significantly more left-wing than the country as a whole, wanting to secede from the rest, partially because they are tired of always having to deal with federal governments that are too right-wing for their taste (despite the fact that in both cases, they really could not complain about underrepresentation in recent governments and had had politicians who became prime minister of the whole country).