I agree that government is social ownership. But it's mainly about the bulk of things. Does the government own 1% of the factories? Probably not really socialism. Does it own 30%? 70%? 99%?
So, to your examples, the government giving out a loan might be considered socialism for that one loan. But what percentage of the banks does the government own? Or, what percentage of the loans does the government originate? Not a very high percentage. (And, when the government takes over a failing bank, they usually do it not to own the bank, but to get it off their hands as soon as they can.) So I don't see lending as being socialism, even if the government does a few loans here and there.
Medicine... there's Medicare and Medicaid. That's not really socialized medicine. How many doctors' offices does the government own? How many hospitals? What's really socialized is a big section of medical insurance.
Another thing that's largely (but not totally) socialized is higher education. Also airports, but not airlines.
So as you look around at, say, the US, it's not really characterized by socialism. It is, to some degree in some sectors, but the whole economy is not characterized by the government owning the means of production.
[Edit: This means that economies are not binary: socialist/not socialist. They are often a mix of some socialism (government ownership) and some not. We call an economy socialist when the government fraction of production (not purchasing) becomes significant, though there is no bright line (above X% it's definitely socialist).]