The difference is how the money is consumed. The fact that the money is collected via payroll is of little relevance.
In an insurance based system theoretically, you can take your money and go to a different provider as long as said provider is happy to treat you for the regulated price.
In Sweden you originally could, then you could not, then you had again "patient choice" in the early 90-es, then you could not and so on. Now you see it, now you do not depending on how "social" is the current party in power. However the option to HAVE this is present and it is an inherent part of the "insurance" style system. That is what the original law of 1946 intended to.
Similarly, theoretically, you can set up a private clinic, pass a few regs and as long as you are happy to treat patients for the amount of money spec-ed by the insurance you can charge that to the national health insurance. AFAIK in Sweden presently, this is mostly theory (but the law actually allows it). In most other EU countries it is the practice and the norm.
UK is a take it or leave it with no such option. NHS is state funded and the option of taking your treatment money and going elsewhere is not available even in theory. Some people tried that one by going to France during the worst years of NHS under Blair. They even sued the UK in the EU court. The end-result is that you can now apply to the NHS itself to have your treatment elsewhere which is from the realm of "yeah, right, not that this will ever happen".
That is the fundamental difference between the rest of EU and the UK.
Anyway, this is all hugely OT.