When Republicans call Norway and Sweden "socialist," are they forgetting that not every business in those countries is government-run?

No, for the most part, conservatives don't know the difference between socialism and communism, and generally point to Venezuela.  They have difficulty with the concept of a mixed system as anything that isn't black and white confuses them. 

Pointless question

Socialism isn't about "government-run". It's about people being paid according to their work, everybody having a job, and the means of production being owned by local collectives.

The nordic countries are Socialdemocrat, which means they are capitalist in a less rabid fashion than the USA, thanks to strong trade-unions and strong moderately leftwing (but to the left of USA Democrats) political parties. Not having first-past-the-post or an electoral college helps..

Like all "rich countries", part of their wealth is due to low wages and lax regulations in "third world countries"

Those republicans are not exactly known for their astuteness.

When Democrats call Norway and Sweden Socialist, do they realize that they are far from Socialist but they are held up by the Democrats as being an ideal Socialist nation?

It’s democrats that point to Scandinavia and claim socialism works, but as you said, they aren’t really socialist, they just have high taxes and less disposable income.  

The former USSR or Venezuela would be much better examples of socialism.  

There are many different degrees of "socialism".  Why are you hung up on republicans and misapplying their opinion.   You seem to not understand that lying is the worse of all, and the democrats intentionally lie a lot.

And so what?

Both countries are mixed economies with a general system of government tending towards the socialist. A model that the dystopic kleptocracy that is today's USA might do well to emulate!

They must not travel much, because anyone who has actually been to Norway or Sweden knows that when you walk down the streets of, say, Stockholm, you see nothing but private businesses and malls just like here.

I think you got that backwards. It's Democrats that refer to the Nordic Countries as Democratic Socialism. Top Swedish politicians have come out and said they are not socialist. They are capitalist with high taxes & a generous social system.