I've seen sed, vērō, and vērum described as "but, butter, buttest," but the descriptions in e.g. Gildersleeve, Bennett—even Zumpt—leave me scratching my head.
Both uero and uerum can often be translated as 'in truth' rather than 'but' in some cases, yielding something stronger than sed. When we have sed, it just means that what we're about to say is different from what we were just talking about in some way. But when we use uero or uerum as in truth, we tie the second sentence more closely to the first. The two situations that come to mind are:
(1) The second sentence contradicts something in the first.
aquam frigidam dixit. uero calida erat.
(2) The second sentences strengthens the first.
aquam tepidam dixit. uero calida erat.
In fact, uerum might be better in (1), because it has a stronger sense of contradiction, but I think the two are mostly interchangeable
However, as pointed out by @cmweimer, these are both commonly used in the same weakened sense as a simple 'sed' or 'at', especially in late classical vulgar latin.
Just to tack on to Mar Johnson's post and our subsequent discussion, the Oxford Classical Dictionary does not support the notion that verum or vero is in itself a stronger contrasting conjunctive than sed. However, the phrase verumvero or verum enim is:
uero, adv., particle.
2 In fact, really, truly.
3 (emphasizing the truth of an assertion) For a certainty, unquestionably, without doubt. b (w. iron force).
uerum, conj [development of ellipt. use of uerum (est) in replies...
1 (assenting to what has been said, but adding a qualification). But at the same time. b (strengthened by uero, enim, or enimuero, ~ uero being also written as one word; see also VERVMTAMEN). c (connecting single words or phrs.). d (in retorts) yes, but. e (with limiting force) but only.
2 (introducing a contrasting fact, idea, etc.) But (on the other hand), however. b (in contrasting an actual with a hypothetical situation, etc.) but in fact, but as matters stand.
3 (after a neg., introducing a contradictory or incompatible fact, argument, etc.) But (on the contrary).
So no, the schema of but, butter, buttest is not actually correct.
The difference between "vero" and "verum" as adversative conjunctions is that "vero", usually at the second place in a clause, indicates smooth transition to something different, contrasting or mildly contrary, without interrupting the narration: it connects rather than separates. Whereas "verum", usually starting a clause, makes a break that finishes the preceding clause and sets the coming clause against it. "Verum" is similar to "sed" in this regard, while "vero" is much like "autem. The "verum"/"vero" pair adds to the "sed"/"autem" pair a sense of assurance or affirmation (due to their primary meaning "in truth"). It is like saying "but forget what I just said and focus on this: ...".
The explanation in Zumpt seems to me pretty helpful (§348): http://www.logicmuseum.com/latin/conjunctions.htm.