While there are many differences between doing research on the internet and doing research at a library, there are similarities as well. This is particularly true if one has access to some of the internet research tools that are commonly provided by universities.
Research in a library typically involves searching for sources on a computerized catalog. The person doing the research then goes and retrieves those sources from the library stacks. This assumes, of course, that the sources are not in use by another patron. This is essentially what a researcher does on the internet. The researcher uses various methods (including searching through library catalogs that are available online) to find sources. The researcher then has to see if the materials are available online. This is the major similarity between the two.
Another similarity is that, in both cases, researchers must pay some degree of attention to how reliable their sources are. This can be more of a problem on the internet, but it can exist in libraries as well. There are many books that have been published whose contents are rather suspect or controversial. Therefore, a researcher cannot simply trust everything they find in a library any more than they can trust everything they find online.