The distinction is not completely bogus but when applied to original documents -- sources -- it is so imprecise as to be useless. It's like claiming that a two-toned car is either red or white.
An original source is a document created at or near the time of the event, in which the event is first reduced to writing. (If five people witness an event and go off and each write their own account of it, those would be five original sources.)
A derivative source is derived from another written source, not from the described events themselves. When confronted with a document, ask yourself, "Where does it come from?" and then look for that document, continuing until you get to the original. When a court record describes a petition submitted by heirs, that description is derived from the original petition. The original petition may contain more information, so you want to find it. As Tom Jones says, every derivative source is an invitation to find out what it was derived from!
Primary information is eyewitness information.
Secondary information is secondhand.
Obviously these overlap; many original documents contain primary information. But the reason for the distinction is that many original documents contain BOTH primary and secondary information. Like the two-toned car, it's only a problem if you don't think it through and use the terms you were taught in high school.
Also obviously, primary information can be right or wrong, and so can secondary. Original documents may contain right information or be a complete tissue of lies. One reason we genealogists prefer original documents is not that they are always right, but that the derivative sources are subject to error in the process of indexing, abstracting, or quoting -- over and above whatever errors might exist in the original.
Finally there is direct evidence (that directly answers your question) and indirect evidence (that provides only a clue toward your answer). So altogether there are eight possible combinations. I word better from examples, hence this table with an example for each.
1. Original source, primary information: Death certificate, cause of death
2. Original source, secondary information: Death certificate, birthplace of father
3. Derivative source, primary information: Published abstract of death certificate, cause of death
4. Derivative source, secondary information: Published abstract of death certificate, birthplace of father
Any of these could be either direct or indirect evidence, because that depends on the question you're asking. If you're wondering what Joe died of, #1 and #3 are direct evidence because they answer your question (rightly or wrongly is a separate issue). If you're wondering whether heart disease ran in Joe's family, #1 and #3 are indirect evidence because they offer a clue without directly answering your question.
If you're wondering where Joe's father was born, #2 and #4 offer direct evidence (again, they may be wildly wrong but they're giving you a direct answer). If you're wondering where Joe's father spent most of his life, #2 and #4 offer indirect evidence -- a hint but not the whole answer.
Harold Henderson, "There Is No Such Thing as a Primary Source," Midwestern Microhistory: A Genealogy Blog, posted 18 October 2012 (http://midwesternmicrohistory.blogspot.com : accessed [access date]). [Please feel free to link to the specific post if you prefer.]