Maxim sounds a bit archaic, I admit I hadn't heard the word before. I think "saying" or "proverb" are more commonly used to mean the same kind of thing Pithy and concise are synonyms, and could be used interchangeably. Both mean "short and sweet, said using a few words with a lot of meaning". Concise is definitely used more, though. I also think that in practice, pithy can have connotations of being "sassier". For example, "he made a pithy comment" suggests he made a quick retort of some kind, whereas "he made a concise comment" just means he said something clearly. "Pith" is the white stuff in the rinds of citrus fruit, so it's something that has a lot of flavour even though there isn't much of it. Hence, "pithy" can describe a short sentence with a lot of meaning behind it