At root we are dealing with a genre of very abstract formal systems. They have grammars that determine their well-formed expressions and rules that determine the permissible transformations among expressions, but they lack all logical meaning until we supply an interpretation.
The formal system Peirce developed for propositional logic and Spencer Brown resurrected for his Laws of Form admits a formal duality that allows it to be fleshed out with logical meanings in two distinct ways. These interpretations are employed in Peirce’s entitative graphs and existential graphs, respectively. It is clear from everything they write that both authors are well aware of both interpretations, but Peirce would come to found his later developments on the existential sense while Spencer Brown favored the entitative sense in his expositions.
See the following readings for further discussion: