The principal distinction between notability and contextual importance/relevance is that the existence of an article on Wikipedia is subject to our notability guidelines, and the notability requirements, in some cases, in our deletion policy; "notability" in Wikipedia does not equate to just a subjective determination of importance, but is based on a criterion of substantial coverage in multiple, independent reliable sources. On the other hand, content in an article that is about a clearly notable subject should itself be of encyclopedic merit, and both relevant to the topic of the article and non-trivial (i.e., important in the context). This relevance and importance determination is not a policy matter, but is a subjective process of editorial judgement, covered in a number of Wikipedia essays.

When you tag an article with {{Notability}}, you are making a policy-based argument that the entire article should be better sourced as something worthy of having an article, or else should be deleted. When you tag something with a relevance/importance template, you are making a copy-editing suggestion. If you argue that something should be deleted from an article because it is "not notable", you are not making a cogent argument. Many, many things important to mention in articles are not independently notable (article-worthy) themselves; e.g. each episode of a TV series, every book written by an author, or every building important to a city. The question is whether including something in the article improves the articles for readers, or mires it in distracting details or asides.

Notability does not even determine whether an entire sub-topical section in an article should be included or not. A very frequent result at Wikipedia:Articles for deletion is to merge a questionably notable topic into an article on a related notable one, as a section.

If you are attempting to flag content in an article on the basis of its importance or relevance to the subject, please use one of the templates below, as appropriate:

Many publications (newspapers, books) and broadcasts (talk shows) and journalists (anchors, reporters) are notable, but they are not necessarily reliable sources from reputable publishers, e.g., various famous tabloid newspapers, talk radio shows, and satire websites; they may be notable for all the wrong reasons. Notability in a Wikipedia context refers specifically to whether a topic can have its own Wikipedia article.

• The Onion is a satirial parody newspaper. While the topic ("The Onion") is notable under WP rules (it has its own article on Wikipedia), the paper is not a reliable source about what it covers, since much of what it says is made up for the purposes of humour.
• Stephen Colbert's satirical news TV broadcasts are a notable TV show, and there is an entire Wikipedia article about these shows. However, the content of Mr. Colbert's shows is not a reliable source about news topics, as the goal of the show is humour.
• A tabloid TV show reporter may have a Wikipedia article about them. While they are notable according to Wikipedia standards, their reporting on celebrity dating gossip ("Foo Barkley was spotted at the Viper Room alongside Fingel Stempleton...dating? Just friends? Friends with benefits") and celebrity substance use gossip ("Foo Barkley was seen outside the XYZ Substance Facility...visiting? Getting treatment? Seeing a friend?") and on alien abduction ("Foo Barkley disappears for 3 days: obviously a case of alien abduction") may not be reliable or accurate.

Many reputable authors (including innumerable journalists and professors), and reliable sources from reputable publishers (e.g., thousands of peer-reviewed academic journals) are not themselves notable – publishing is not the same thing as being covered in-depth as a subject in other independent, reliable publications.

If you argue whether a source should be used based on whether it or its producers are "notable", or insist that a particular researcher or journal must be notable because it is reputable, you are mixing apples and oranges. First of all, WP:Notability is a policy regarding whether a given topic is worthy of its own article in Wikipedia. The sources (authors, scholars) whose publications are used to support a claim that person X or topic Y are notable do not themselves need to be notable. (It doesn't harm your case if these authors and scholars have been deemed notable in Wikipedia, but this is not required).

The only connection between the concepts is that reputability (a large part of reliability) is often discernible in part through independent coverage. This can be misleading, however. For example, a scientist very famous as an educational TV show host may not be particularly eminent in actual scientific publishing; likewise, a young journalist at a paper with an large international readership, and who won an award once for a controversial society piece, may not be as reliable as a twenty-year professional at a national business and finance newspaper, especially if the topic is interest rates rather than gender imbalance in the tech industry.

From a more philosophical perspective, notability is also not entirely objective; necessarily permanent; judged in isolation; nor based on merit; these points are covered in detail at the essay WP:What notability is not. It is also said that notability is not a level playing field, nor just a matter of opinion.

It can even be argued that Wikipedia's Notability requirements are not even "fair", in that a reality TV contestant who gained notoriety for their offensive views on Celebrity Substance Use Exploitation (a fictional TV show!) over a 30 day period may be deemed Notable, but a voluntary sector leader who dedicated their life to helping children, over a 30 year period, may be deemed "Non-Notable", if the former has 100s of articles about them in newspapers and magazines and the latter has only one article in the newspaper.