Q. What are the differences between primary/secondary and scholarly/popular sources?

In general, scholarly sources are those published by and/or for experts and/or scholars--experts in a particular field or area of study.

We most often explain this in terms of articles....scholarly articles are published in scholarly/academic journals, and they are usually based on some actual research (case study, experiment, trial, etc.). They are usually written by experts in the field for other experts in that or a related field, or people who are studying to become experts (scholars) in that or a related field. And in many disciplines, this research (and even the articles themselves) are considered primary sources. Textbooks, on the other hand, would be considered scholarly, but they would be secondary sources, not primary.

(The other types of articles commonly used in information seeking are those published in magazines and newspapers; we refer to those as popular periodicals because in general, they appeal to anyone...you don't have to be an expert or have any particular specialized knowledge in order to read them.)

Primary versus secondary sources is a little more complex. What constitutes a primary source is often different depending on the field you're in. An example in biology might be a lab report (a write-up by a scientist about the results of an experiment); this can also, if it's fleshed out into a full article, be considered a scholarly source (and published as an article in a scholarly journal). In the social sciences, a primary source might be a diary, a letter or even a newspaper article written by somebody who experienced an event (in the case of political science, for example).

So, the answer to your question - how are primary and scholarly sources different - really depends on what class and/or what topic you're researching. Check the links below for more information. 

Ultimately, it will be up to your professor for each class to determine whether or not a source fits his/her idea of primary/secondary, popular/scholarly.