This begs the question: are they really different operators, or are you just writing the same operator in a different orientation? The fact that we type them differently is perhaps an artifact of the way we encode text on computers. We don't represent characters as a codepoint+rotation duple; instead, we can only record different characters, with a different glyph for every orientation.
"=" is the only relational operator which is commutative. a = b implies b = a.
= (Slashdot filters out the single glyph representation of this operator, U+2264) is not commutative. a = b does not imply (or preclude) b = a.
Is there a name for the property of "" which is that a b implies !(b a)? You could call that operator "anti-commutative", perhaps?