Difference between symmetry and symmetrize? so if I were to make a human head, with symmetrize, you only need to make half of the face?

With symmetry enabled, all you sculpt on a side will be sculpted on the other side according to the symmetry axis you choose (important to note that the symmetry move through the Origin of the object, so make sure the Origin point is at the symmetrical center of your object)

Now the Symmetrize function will port everything from one side of the symmetry to the other side (according to the direction you setup).
By example with direction “+X to -X” :

remember the Origin point of your object is still the center of the symmetrical axis that you’ll use there too, you can get some fun result depending on where you move the origin point

Okay so symmetry is like real time? And if I use symmetrize, I only have to create half of the face?

nope, symmetry is used during polymodeling task.
Symmetryze is a special tool of Dynamic Topology.

I see, poly modeling is like extreme details yes? (having more subdivisions in a mesh)

If you’re sculpting, Symmetry is real time.
Poly modelling is when you work in Edit Mode and require the mirror modifier to get your modelling being mirrored at real time.
There was a X-mirror option but never managed to get it to work reliably in Edit Mode

Symmetrize in Edit Mode ( W -> Symmetrize) works similarly to the one in Sculpt mode

Okay thanks, but can’t I just use the mirror modifier? what difference is there to that?

It depends on what you actually want to do, if you want to model in edit mode, using the mirror modifier is a good idea.
If you want to sculpt, use the Symmetry X/Y/Z option, not the mirror modifier because it will only lead into problems (both in Dyntopo or in Multires), just try and see what happens.

Alright thanks!

Symmetrization is a process that converts any function in n variables to a symmetric function in n variables.
Symmetry is the quality of being made up of exactly similar parts facing each other or around an axis