I've basically always used these words synonymously. Can someone elaborate on whether there is a difference?
Typically the word "righteous" or "just" are simply alternative translations of the same word, "dikaios" (δικαιος and cognate verbs and such). There is simply no difference.
I'll go ahead and add an analogous example that people also often confuse, and that is the difference between "faith" and "belief". In Greek they are translations of the same root. In English, you don't say "I faith (verb) in something" but you would say "I believe (verb) in something". But you would say as Jude does and call something "the faith (noun) once and for all delivered". You could add a helper verb to make faith work verbally like "I have faith in God". But all that is just English usage. In Greek the verbs/nouns/adjectives are all built off the same root, "pist-" (πιστ-) and mean the same thing.