Imagine the Earth is a big ball and the ocean is a thin layer of water covering it. Now, the moon, which is a smaller ball in the sky, has a type of “pull” (we call this gravity) that it uses to attract things towards it. This pull is stronger on things that are closer to it and weaker on things that are farther away.
So, when the moon is above a specific part of the Earth, it’s pulling on the water there more strongly than on the water on the other side of the Earth. This causes the water to bulge out a bit towards the moon, creating a high tide.
But why is there also a high tide on the other side of Earth, farthest from the moon? That’s because the moon’s gravity is also pulling on the Earth itself, but not as strongly on the water on the far side. That water gets “left behind” a bit, creating another bulge and another high tide.
As the Earth rotates, different parts of the Earth pass under the moon, so the bulges (the high tides) move around the Earth. That’s why most places on Earth see two high tides and two low tides every day.
> would their still be a height difference without lunar tides?
Yes. Winds also shape the surface of the seawater somewhat and consistent wind patterns effectively create ‘hills’ of seawater over many kilometres laterally, though they are only metres high at the most.
We can average out both the effects of winds and tides with satellite altimetry though (given enough passes over the whole Earth from satellites in different orbits). Even then, there is a difference between different parts of the world because (1) the Earth is an oblate spheroid so water bunches up nearer the equator, (2) the strength of the gravity field does not just follow a simple shape based on (1) because different rocks have different densities and there are also lumps/bumps in the seafloor (not to mention continents surrounding ocean basins). These all contribute a bit more or less to the gravity at any one point, so the [resulting reference shape of sea level](https://en.wikipedia.org/wiki/Geoid) is lumpy, but only by a 200 metres when comparing absolute lowest and highest bits. So it’s still incredibly smooth on the scale of the whole Earth, but it’s far from perfectly smooth. (3) Different ocean basins are underlain by different tectonic plates, with different spreading (or subduction) rates. The newer a portion of oceanic crust is, the hotter and more buoyant it is, so that it sits higher in the underlying mantle. This creates a higher sea level when measuring as distance from centre of the Earth.
There’s a nice answer on r/askscience which I think is actually very Eli5 friendly and goes through the different reasons why [here](https://reddit.com/r/askscience/comments/143xu8a/is_0_elevation_sea_level_the_same_everywhere/jne8dnb) Important for these sorts of questions is what you want to use as a reference point to start measuring from. In most cases, the geoid is the best reference for zero sea level.
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