As is clear in the posuk, the baker only approached Yosef for an interpretation of his dream upon seeing the butler coming out with good news.
Seeing this it is safe to differentiate between the baker and the butler in that the butler was seeking the true message of his dream whereas the baker was going for the good news only, which means he was masquerading, pretending to be an innocent person seeking for the message relayed to him when in truth he was not which made him a liar.
It is important to note that when the Torah tells of someone lying or any other trait be it good or bad, it is a deeply rooted attribute of that person.For the Torah is very relevant and concise and in a posuk or two the Torah brings out the essence of the person spoken about. This is as we see that the Torah highlights Avraham's attribute of Chesed in a mere few pesukim and in Chazal's eyes it is this facet and virtue which stood as his merit forever.
The Midrash Bereishit Rabba (19:2) points out four that began their remark with the word 'Aff' meaning anger and were lost with that word, one of them being our baker. Now see the pirush Maharza'v on the Midrash who explains that these four were up to cruelty which brought this terminology to their tongue's. This illustrates to us how Chazal took every word that any character uttered and used that to explain their entire predicament.
Well, the posuk in Shmuel b' 22' says "with a crook act crooked".Yosef, replying to the baker's dishonest request in searching for the dream's true meaning, answered him accordingly, by appearing as though ready to glorify his quest for the good news.
Another understanding; the butler dreamt that he was serving the king again which meant that this was good news for him whereas the baker would not even dream of baking for the king again, as we do not see him dreaming that he carried the food to the king, showing us all that good news for him was anything but serving the king again