A non-Fregean framework aims to provide a formal tool for reasoning about semantic denotations of sentences and their interactions. Extending a logic to its non-Fregean version involves introducing a new connective$$\equiv $$≡that allows to separate denotations of sentences from their logical values. Intuitively,$$\equiv $$≡combines two sentences$$\varphi $$φand$$\psi $$ψinto a true one whenever$$\varphi $$φand$$\psi $$ψhave the same semantic correlates, describe the same situations, or have the same content or meaning. The paper aims to compare non-Fregean paraconsistent Grzegorczyk’s logics (Logic of Descriptions$$\textsf{LD}$$LD, (...) Logic of Descriptions with Suszko’s Axioms$$\textsf{LDS}$$LDS, Logic of Equimeaning$$\textsf{LDE}$$LDE) with non-Fregean versions of certain well-known paraconsistent logics (Jaśkowski’s Discussive Logic$$\textsf{D}_2$$D2, Logic of Paradox$$\textsf{LP}$$LP, Logics of Formal Inconsistency$$\textsf{LFI}{1}$$LFI1and$$\textsf{LFI}{2}$$LFI2). We prove that Grzegorczyk’s logics are either weaker than or incomparable to non-Fregean extensions of$$\textsf{LP}$$LP,$$\textsf{LFI}{1}$$LFI1,$$\textsf{LFI}{2}$$LFI2. Furthermore, we show that non-Fregean extensions of$$\textsf{LP}$$LP,$$\textsf{LFI}{1}$$LFI1,$$\textsf{LFI}{2}$$LFI2, and$$\textsf{D}_2$$D2are more expressive than their original counterparts. Our results highlight that the non-Fregean connective$$\equiv $$≡can serve as a tool for expressing various properties of the ontology underlying the logics under consideration. (shrink)