In many ways, it doesn’t. We both profess the truly Real Presence. Non-Christians often are entirely oblivious to the subtle differences, and some Protestants like to poke Lutherans for “basically being Papists.” But the difference is significant enough to keep our communions separate, and more “old fashioned” Lutherans will make sure you know that.
No Lutheran, if he is catechized, should ever think that Jesus is in any way confined inside the bread, as if he were filling the holes in Swiss Cheese or stuck inside the bread through impanation. We know only what Jesus told us; that “This [bread] is my Body.” We put a period there and simply accept the incomprehensible mystery of Christ’s words. Catholicism, in a well-meaning attempt to make this miracle make sense to the laity, places a comma and explains that the Bread actually stops being bread – but Christ never said that.
It’s actually a moot question to Lutherans. Our pastors only consecrate the bread and wine when it is intended to be eaten – during the Divine Service. We take Christ seriously when He said, “Take and eat.” He did not tell us to save some in a bowl for later. During the service, our elders carefully count the number in attendance so that no more is consecrated than necessary. Lutheran practice is to consume everything during communion.
On the rare occasion that any remains, it is kept separate from the unconsecrated. Again, we take Christ seriously – He never said whether His Presence persists or not, so we play it safe and assume it does, treating any remaining with due reverence.
A previous post of mine might help to explain. A real-life example: a shaking, elderly Luther once spilled some of the cup while communing his flock. He knelt to the ground and lapped up the Blood like a dog. The congregation was so moved, they burst into tears. On another occasion, when another pastor spilled on the altar and could not remove the stain, Luther cut out the portion of the Altar and had it burned, according to the ancient custom of burning the remains.