Being the closer is different. Being the guy asked to get the last three outs of a game increases the degree of difficulty, frays the nerves and makes the heart beat faster.
Sure, you can debate the significance of the closer role as many have in recent years. Doesn’t the guy who faces the heart of an opposition’s batting order in the eighth inning deserve more credit than the guy who faces the bottom of the order in the ninth? Shouldn’t you use your best reliever against the opposition’s best hitters? How good does a closer have to be to record a save with a three-run lead?