PRECISE DPLL algorithm definition
What you are finding is that there are multiple versions of DPLL, all of which might have the name DPLL attached to them, even though they are a little different in some specifics.  If you need to distinguish between them, then I suggest you introduce your own terminology.  I don't think it really matters which one you call the &quot;one true DPLL algorithm&quot;.  If you have to pick one, you could use the specification in the original paper, but I suspect it's probably best to understand &quot;DPLL&quot; as referring to a family of closely related algorithms that are very similar to each other but not identical.
&quot;backtracking + unit propagation&quot; is not a definition of an algorithm; it is at best a high-level summary.