5.56 is the bullet diameter, 45 is the case length - both in millimeters. As you stated, it's hotter than the .223 and that's the main difference - a 5.56 chamber is rated for higher pressure. Same goes for 7.62x51, 7.62x39, 7.62x54, 5.45x39 - bullet diameter followed by case length. More @Wikipedia
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