ANSWER: Only two of the four gospels, Matthew and Mark, mention Jesus being offered something to drink before being placed on the cross. Matthew 27:33 - 34 refers to this drink as wine mixed with gall, while Mark calls it wine and myrrh (Mark 15:23). Both Biblical verses refer to the same thing.
33 They came to a place called Golgotha, which means, 'The Place of the Skull.' 34 There they offered Jesus wine mixed with a bitter substance (most translations have 'gall'); but after tasting it, he would not drink it (Matthew 27:33 - 34)
Jesus was offered a wine and gall mix to drink just before 9 am on Wednesday, April 5 in 30 A.D. The offering took place right after he arrived at Golgotha but before he was nailed to the cross and the Roman soldiers cast lots for his clothes.
The English word gall, in the New Testament, comes from the Greek word chole (Strong's Concordance #G5521) which literally means poison. All the Old Testament verses that use this word (Lamentations 3:5, 3:19, Jeremiah 8:14, 9:15, 23:15 and so on) have a common definition of something that tastes bitter and is (many times) poisonous.
A mixture of wine and gall was commonly given to criminals before their execution in order to ease some of their suffering. As an ex-chemistry teacher, I taught in my classes that all poisons are BITTER but acids are SOUR. Christ likely refused this drink knowing that its bitter taste meant it was more of a poison than a pain killer. He did not want to die from poisoning or have his senses numbed while on the cross. He knew that He had to shed his blood in order for Him to become the supreme sacrifice for the sins of all man, and He refused to take the easy way out of it.
The offering of this concoction by the Romans, however, was a fulfillment of a prophecy given by King David. While in the depths of a painful trial David cried that his enemies gave him only something bitter to quench his thirst (Psalm 69:16 - 21).
After hanging and suffering on the cross for six hours, in the heat of the day, Matthew 27 and John 19 tells us what ultimately ended the life of man's Savior. His suffering quickly ended after a Roman soldier plunged a spear into His side, causing both blood and water to come out of the wound. This stab also fulfilled Bible prophecy (Zechariah 12:10).
"Then another took a spear and thrust it into His side, and out came water and blood. And after crying out again with a loud voice, Jesus yielded up His spirit." (Matthew 27:48 - 50, Holy Bible in Its Original Order)
Thank you for your question about wine mixed with gall.