Are there any terms used to describe the conversion of a noun into an adjective and vica versa?
redundant -> redundancy
Synonyms are when two words mean the same thing. Is there a term similar to this for these purposes?
The process of changing a word with one grammatical function into a word with a similar meaning but a different function is called Derivation.
Derivation one of the two varieties of Morphology (the other is Inflection). English has almost no inflection left, so its morphology is almost all derivation, and quite a lot of that is Zero Derivation, where there's no suffix (He's growing like a weed vs. I have to weed the garden)
The specific term for turning a word into an adjective is adjectivization. Nominalization (or substantivation ) is the process of turning a word into a noun.