Cast metal is an object that has been made by pouring molten metals into a mold. Machined metal is a form that is cut out of a solid peace.
Ill explain a little further, I used to work in a foundry.
First the master is made; this is the exact shape of what the product is supposed to look like. It is either carved out of solid steal or plastic and are called “tools”. These hollow forms are then filled with wax, these forms are then dipped into slurry and various sands. The sandy wax mold is then put into a large auto-clave and all the wax is melted out.
Next the molds go through a huge oven where they are brought up to temperature; from there they are quickly taken out of the oven, sat in a cart and filled with molten metal. From there they go to knock out where the shell is broke off with basically a huge squirt gun. Then the trees are cut off the molds. Next comes various stages of finishing including sanding, tolerance and clearance test, x-ray tests and slew of other rigorous tests.
There are a few others forms of this process but they are all basically the same basic idea.
As for machining, the metal starts as a block form, attained from a foundry where it was poured into this shape. The blocks are put into various machines like CNC, mills, lathes, stampers, formers to achieve the design...etc. etc... Hope that all makes sense.