3.5.0 Alpha version of Blender

There is no difference in the Edit Mode Mirroring in 3.5, compared to earlier versions.

If a Vertex is slightly moved on one side of the Mesh, compared to that 'same' Vertex on the other side, Then Symmetry won't work for that Vertex. If the Topology is still the same on each side of the Mesh, it might work with Topology Mirror enabled.

But I wouldn't rely on it; use the Mirror Modifier instead.

Just in case you are wondering what Topology is; think of it like this, if you only Move Vertices around, you are not changing the Topology of a Mesh.

I got more confused with that definition of topology. I thought topology was how vertices were placed in edit mode, and if I moved vertices around I would change the topology of the mesh. Explain it to me like I'm 5 please.

I don't think I can explain it to a 5 yr old...

Simply said, you were wrong. Moving Vertices in Edit Mode doesn't change the Topology. CG Meshes are 'made of rubber' and can be deformed, streched and so on. That doesn't change the Topology:

Like In Sculpt Mode. Sculpting by default doesn't change the Topology of a Mesh, only it's shape.

Unless you activate Dynamic Topology (changes the Topology dynamically), or use a Multiresolution modifier.

Ah I see what you mean. You see, you did explain it to me like I'm 5. 

So the topology is more like the orderly fashion the vertices are in. It's like what molecules are to an element. H2o is H2o, it's two hydrogen atoms and one oxygen atom, and yet you can have water in a glass and it will take the shape of the container. The shape will change but it's still H2o. 

With Topology Mirror enabled, Blenderr can find the corresponding Vertex on the other side of the monkey: