I've seen a lot of answers in this subreddit be removed if they are an anecdote about the historical subject that is asked about, even if the person has lived through the specific event him or herself. This got me thinking, aren't most primary sources an anecdote of some sort? I can see that you would want to collect a large number of personal accounts to get a proper understanding of an event, but doesn't that mean that every individual anecdote has historical value?
In brief, as enforced on the subreddit the difference is about context, and primarily aimed at where the end point is "anonymous person posting on an internet forum claims this". Primary sources often are in many ways quite similar in their content, but there is still a world of difference between the two in how we, as historians, can evaluate them and contextualize them. For more than the TLDR here, this Rules Roundtable is a much more exhaustive explanation.
I wanted to throw something in the mix that is a little bit outside the scope of your question but it's a tension that comes up constantly in education history and I suspect, other fields. And it's basically, mention of something in a primary source doesn't mean the description accurately reflects the historical record and the absence of something in the historical record doesn't necessarily mean it didn't happen in the past.
As a context for the former, as the American teaching profession feminized, a class of administrators - known as schoolmen - emerged. They lead buildings, districts, and states and spend a great deal of time trying to impress each other. Which means they wrote thousands, if not millions, of words about schools, students, teachers, curriculum, and more. In some cases, their words reflected what was happening in classrooms. In others, they were speculating wildly and pontificating. The consequence of this as more historical texts are digitized is that it's fairly easy to develop a theory about the history of education and find a schoolman who said something at a conference or wrote something that affirms that theory. And yet, just because a schoolman wrote it doesn't mean it translated into changes at the school or classroom level.
This is, in effect, the inverse of what's been happening of late regarding abortion in American history. As an example, two law students - with zero training in histography or abortion history - recently published a paper claiming there was no "right" to abortion in American history because they couldn't find evidence of people talking about it in historical documents. As expected, historians of women's health and sexuality (rightly) expressed deep frustration.
Which is to say, it can often be even more complicated than what's in - or missing from - primary sources.