What is the relationship between syntagmatic and paradigmatic?

They are the two relationships between linguistic elements that define how language works, according to structuralism. They are complementary.

The syntagmatic relationship is how linguistic elements can be sequenced. It’s syntax. And morphology. And phonotactics.

The paradigmatic relationship is which linguistic elements behave in the same way in syntagmatic relationships. It’s lexicon. And phonetics. And the… other bit of morphology.

The syntagmatic relationship gives you the structure of language; the paradigmatic relationship defines the function of individual bits of language.