What we understand by Popularity
- page / web site authority (PageRank for Google) calculated by the Search Engine
- social media impact
In short phrase: Popularity is what is measured outside your web site, how others see you. This is determined by comparing your metrics with other web sites from the same category as yours.
Couple of Relevance factors
- content (the quality of your page overall: information, page source etc.)
- language (declared page / web site language)
- domain / link name
In short: Relevance is what you can measure in your own page or web site. This is calculated by comparing your information with other information from relevant sources.
If for Relevance you can do something about it immediately (Conduct a keyword research and improve the quality of your content), then for Popularity is a bit different. Factors like authority and page rank are impossible to change in a short period of time, all you are left with is to work on Social Media impact. But don’t get me wrong: this can be very time consuming and costly too.