(Moved from mathoverflow as considered not researchy enough)
This came up via someone proposing a change from a $A \leq B \leq C$ in a computer graphics API specification to $A' \eqslantless B' \eqslantless C'$, where A/B/C are all scalar real expressions or variables, and the A'/B'/C' expressions were simple variants of their non-primed counterparts. I have been unable to get clarification from the person proposing this change.
At first this appeared a simple question; Unicode defines the symbol as "equal to or less-than", which would appear to be the same as "less-than or equal to". But on investigating a bit, I found very few uses or definitions of this symbol in online mathematical literature. Google Books (see link) turns up a variety of use cases in such diverse fields as automotive chassis, logic, public economics, quantum electronics, and theoretical computer science - but virtually every use appears to be accompanied by its own, inconsistent definition of the meaning. General web searches turn up almost nothing relevant. People have suggested this is an archaic synonym for $\leq$ that's fallen out of use, but I've found no evidence to support that. Still, it found its way into LaTeX AMSmath and Unicode somehow and presumably has some documented history somewhere.