They're the same, because the chapter headings say so

If you've grown up in church, you probably know about Jesus cleansing the temple. An account of it appears in all 4 gospels: in the three synoptic gospels (Matthew, Mark, and Luke), it appears after the Triumphal Entry, during the last week of Jesus' life. John, however, puts the cleansing of the temple at the very beginning of Jesus' ministry, immediately following his first miracle. If you were just skimming the Bible, reading the helpful little subheadings the editors of your particular translation have put in, you would see that both were labeled "Jesus cleanses the temple" or "The cleansing of the temple." And you would be excused for thinking that they were accounts of the same incident, that John had merely moved it to make some kind of point. In reality, though, the event recorded in John is vastly different from that recorded by the synoptics, and there is no reason to conflate (combine) the two. It makes about as much sense as seeing the boyhood journey of Jesus to Jerusalem in Luke and identifying it with the Last Supper in Matthew, which is no sense at all.

There are only two reasons to conflate the two events, and neither of them are good. The first is that they are superficially similar: they look the same if you only read the extra-biblical chapter heading. This is not a good reason, and we'll explore this further in the next couple paragraphs. The second is a really strange assumption that Jesus only ever went to Jerusalem for passover once. This is completely incorrect: for Jesus to be a good Jew, and we know that he was, he would have had to take passover at Jerusalem every year. Which means that according to most models of his earthly ministry, he would have taken his disciples to Jerusalem at least 3 times, only the last of which included the palm branches, hosannas, etc. So before we see the chapter headings and assume they're the same, let's investigate the events themselves.

Let's do the synoptics first. Mark gives us the most complete account, telling us that after Jesus made it into Jerusalem after the triumphal entry, it was already late, so the cleansing of the temple occurred the next day, probably in the morning (Mark 11). In all three accounts, Jesus makes reference to Isaiah 56:7: "For my house shall be called a house of prayer for all peoples." He also refers to Jeremiah 7:11, which accuses Israel of making the temple into a "den of thieves." So he quotes the same two scriptures in all three accounts. Next important thing: immediately following the cleansing, nobody challenges him. At all. The pharisees are furious with him, but they can't do jack to him: after all, he was just praised as the conquering king from YAHWEH himself. In Matthew 21 and Mark 11, the pharisees wait a full day before coming to him with a question: "By what authority are you doing these things?" Jesus answers with a trick question about John the Baptist, owning the pharisees so hard that the only answer they can come up with is "We don't know." Jesus basically says, "Well, since you didn't answer my question, I won't answer yours."

Now let's look at John. John doesn't connect this with the triumphal entry at all. In fact, he seems to connect it with an entirely different trip to Jerusalem: an earlier one, when people were just beginning to believe in him because of his great deeds (John 2-3). There is literally no hint at all, other than the extra-biblical label "Jesus cleanses the temple," that this is the same event recorded in Matthew, Mark, and Luke. Let's go further. Take a look at what Jesus says: "Take these things away; do not make my Father's house a house of trade." Again, this sounds superficially similar to what he says in the synoptics, but it is completely different. This is not scripture: it is Christ's own words, unquoted from anything else. It mentions neither a house of worship nor a den of thieves. And this sparks a remembrance by the disciples that isn't found in any of the 3 synoptics: the disciples remembered "that it was written, 'Zeal for your house will consume me.'" Then the Jews challenge him, apparently immediately after he's driven out the money-changers and animals. They ask, "What sign do you show us for doing these things?" Jesus answers, "Destroy this temple, and in three days I will raise it up." This is a completely different challenge, and a completely different answer, than the one found in the synoptics.

Let's review. In the synoptics, the event is explicitly linked to the triumphal entry: in John it is not, and seems to be linked to a different trip to Jerusalem. In the synoptics, Jesus quotes scripture, mentioning a house of worship and a den of thieves: in John, Jesus doesn't quote anything, and mentions neither a house of worship nor a den of thieves.  In the synoptics, it is quite clear that the objections come a day later: in John, it seems to be immediate. The objection found in the synoptics is completely different from that found in John: the answers, likewise, are completely different. So literally every single aspect of the event found in John, except for the extremely broad "Jesus cleanses the temple," differs from the account found in the synoptics. Why would we ever assume that they're the same event? It makes about as much sense to look at Luke 2:41-50, see that Jesus is teaching in the temple, and assume it's the same event as that found in John 12:20-42, because they both take place in Jerusalem when Jesus is teaching and astonishing people.