Technically, this is no different. However, in practice I can understand if EU people had a motive to try to keep member countries in one piece (Catalonia is next in line). And if EU now decides to take its gloves off, it can "easily"[1] tell that Scotland or any other part of UK is very welcome to stay in EU if they so wish. It would be interesting times on the British side of the negotiation table once Scotland, Wales, North Ireland and City of London decide to split from UK and into EU...
[1] I am no lawyer nor politician, I have no idea how easy this would be from any practical point of view
the thought of the vast majority of EU countries approving EU membership for an independent Scotland and Spain vetoing it because of implications for its internal politics is an interesting one I hadn't thought of...
Venice want to become a city-state republic again, and the Italian islands also made moves about wanting independence.
Italy is very aware of this, and in the past last time someone tried a independence stunt (some guy built a artificial island and declared independence) Italy bombed the shit out it.
Italian and Spanish "estabilishment" politicians are probably panicking now, since independence movements might consider UK leaving the EU, and the potential for Scotland to leave UK, "inspiration" to make their own moves.
Wales is little England†, the Welsh voted overwhelmingly to leave. Check the stats again. You're right Scotland and Northern Ireland though. Also the City of London is the small Square Mile at the heart of London geographic area where all the finance happens, that big round thing roughly coinciding with the M25 orbital motorway is called Greater London or just London! :)
† This is not meant as a nationalist slur, or a conflation of identities - it is meant in terms of political sentiments and voting patterns. Scotland and Northern Ireland are far more devolved.
[1] I am no lawyer nor politician, I have no idea how easy this would be from any practical point of view