Structuralism is an ambiguous term. The positive side of it to shift analysis/critique towards looking at how physical and social relations shape ideas and language, rather than assuming they can have a priori causa suis. The negative side, is a kind of linguistic determinism, that'remeniscent of historical materialism.
A Structuralist is most of all trying to reveal hidden structures, like say Lacan uses psychoanalysis to understand social forces. I would describe that as looking for new or previously unrecognised patterns. Categorising and classifying are just tools that may help find, or provide evidence for patterns. To say all so doing is Structualist would be to extend the meaning of that term vastly beyond how it is actually applied (a category error, ironically).
I would describe Post-Structuralism as the rejection of the universality or absoluteness, of implications drawn from analysing the influence of languave and the structures of our thoughts, on culture. A rejectiin of linguistic determinism. Not of categories.
There are certainly traditions which so aim: Philosophers or philosophical traditions that reject symbolic reasoning
Deleuze was specifically targeting the implicit idea of a binary discourse making up the dialectic, a pure thesis meets a defined antithesis, with a single coherent result. He wanted a live mapping including many aspects of connection, rather than a tracing which imposes a specific dimension to the abstractions and discards the rest. His picture of the rhizome, is like what we now call intertextuality, a refusal to accept a single set of typologies or relationships.
I would relate Structuralism and Post-Structuralism to the ghost of Hegel. There was an appealing simplicity and certainty to it that led to believing in a kind of 'psychohistory', a hidden cultural determinism philosophers can reveal. But the problem was, picking one way to view the historical/cultural narrative as the only significant one, closes off other stories. It is the tension between holding up the significance of a lesson we should learn, and recognising there are lessons we are not yet ready to learn from the same history. Good historians probe and reframe the categories of their discipline, how we group events together, and so on. I would describe Structuralists as believing there will in the end be one history, even if it's a rhizome not a tree, and Post-Structuralists as recognising the historian is part of history too.
