Definition
Magnitude is the single, fixed amount of energy an earthquake releases at its source, while intensity is how strongly the ground shakes and how much damage occurs at the spot where you are. Think of a light bulb in the middle of a room: the power it uses is one fixed number, but how bright it looks depends on which corner you're standing in.
A speaker's volume vs. what your ears hear
Picture a huge speaker at an outdoor concert, playing music at a steady level. The total sound energy that machine puts out is just one number. That's like an earthquake's magnitude, the size of its energy. It tells you how much energy burst out at the focus, deep underground where the quake began. No matter where you measure it, magnitude is one number.
But what the audience hears depends on where they sit. Someone in the front row gets a deafening roar. Someone in the back row, or far outside the venue, hears only a faint sound. How strongly the ground shakes where you are works the same way, and that's called intensity.
So when one earthquake strikes, only 1 magnitude number is announced for the whole country. Intensity, though, is reported separately for each place, such as Seoul, Daejeon, and Busan, and the numbers can all be different.
A little more precisely
Magnitude is written as a regular number with a decimal point, like magnitude 5.4. Scientists use the Richter scale, named after the American seismologist Charles Richter, or the moment magnitude scale, which is calculated from things like the area of the fault that slipped and how far it moved. The key thing to remember is that every time magnitude goes up by 1, the energy released grows about 32 times, exponentially. A magnitude 6 quake isn't just a bit stronger than a magnitude 5. It holds 32 times more energy.
Intensity, on the other hand, is a whole number based on what people feel and how much buildings are damaged. It's usually written in Roman numerals (for example, intensity IV or VII), and the scale differs from country to country. Korea uses the 12-level Modified Mercalli Intensity scale, which was developed in the United States, while Japan uses its own 10-level scale.
Intensity usually gets lower the farther you are from the epicenter, the point on the surface right above where the quake began. But soft soil amplifies shaking more than solid bedrock does. So even far from the epicenter, intensity can come out high depending on ground conditions.
Why does intensity matter more to us?
When you get an emergency alert on your phone, you don't need to feel too relieved or too scared just because of the magnitude number. Say a huge magnitude 7.0 quake strikes deep under the sea, but it's thousands of kilometers from your town. The intensity you feel might be just I, the lowest level, with almost no damage from shaking. One caution: an undersea quake can also cause a tsunami, separate from the shaking, so intensity alone can't tell you the danger along the coast.
Now flip it around. A quake of only magnitude 4.5 can still reach intensity V to VI if it's shallow and right under your town. Things can fall over and walls can crack. That's why, when deciding whether to send alerts or when estimating damage, officials pay close attention to the intensity in each area.
Earthquake-resistant building design also depends not on magnitude but on how hard the ground will shake at that exact spot. For that, engineers use ground acceleration values instead of intensity levels.
Common misconceptions
A magnitude 6.0 earthquake is only about 1.2 times stronger than a magnitude 5.0 one.
Magnitude is a logarithmic scale, so each step up means about 32 times more energy. A difference of 2 steps means roughly 1,000 times more energy (32 × 32).
If one earthquake produces several different intensity numbers, someone must have made a measurement error.
An earthquake has just 1 magnitude (its total energy), but intensity (the shaking people feel) naturally differs from place to place depending on distance from the epicenter and ground conditions.
Where you meet it
A big magnitude 7.0 quake struck far out at sea, but it was so far from land that coastal cities felt only weak shaking at intensity II. Even so, a tsunami can still form separately, even when the shaking is weak.
It was only a magnitude 4.5 quake, but it was shallow, just 5 km deep, so a village right near the epicenter felt intensity VI shaking and suffered some damage.
In one sentence
Magnitude is the absolute amount of energy an earthquake releases, while intensity is how strong the shaking and damage actually were where you are.