http://www.logic-alphabet.net/images/flipstick_2347_2.jpg
Both are systems of symbols meant to encode 4 bits of information. In both cases, pointy bits in the corners of the symbols represent 1 or true, while round bits are 0 or false.
A difference is that in the case of bibi-binary the intent is to encode numbers, while the intent of the logic alphabet is to encode truth tables of binary logic operators. But fundamentally they encode the same information.
The other difference is that the inventor of bibi-binary was a comedian who obviously did it as a tongue-in-cheek novelty, while the logic alphabet's creator appears to have been quite convinced of the importance of his invention...