Create liquid inside a glass

I am trying to fill a glass with milk.

First of all my blender doesn’t have an Inflow option to make fluids, but for now I am just gonna stick to make a static liquid.

So it shouldn’t be too hard but I am really struggling for some reason.
When I copy the inside of the glass and duplicate it, even if I separate the objects, they still kinda interact with each other, like if I change material to one, the other will change.

How do I do?

Duplicate part of the inside of the glass with Shift+D, right mouse to leave in place, then immediately press P and chose Selection to separate that part to a new object. It will still share the same material as the glass. Delete that material in the liquid object and add a new one.

You have the same material linked to both meshes. Click on the number next to material name (it probably shows 2 or some higher value), it will make an unique copy of the material. That number tells you how many users a linked instance has, clicking on it makes it unique. Works the same with all data in Blender, meshes, textures, materials etc.