Translation:I need to discuss something with you.
Would the Chinese be different for "I want to discuss ..." than for "I have to/need to discuss ..."?
Yes, since 要 can be both "want" and "will", you need to replace it with other words.
我想…… I want to ...
我需要…… I need to ...
我必须…… I have to ...
So does that mean that this question can also correctly be translated into "I want to discuss something with you"?
Sure it can (reported), but you don't have to replace it with a less ambiguous word unless it is important for disambiguation.
"have to/need to" would be more like 需要. If you put "want to", it should have been accepted.