Is acetate the same as wool?

No, acetate is pretty much the opposite of wool.

Acetate is a man-made fiber made from plant cellulose, and takes dyes as such, (procion, fiber-reactive). It's not a synthetic in the polyester (plastic) category. but it is man-made.

Wool and silk are protein based natural fibers; acid dyes are best when dying these fabrics.

Acetate is a cool fiber as opposed to warm wool. It is generally used to make smooth, glossy and light weight fabrics for linings.

Wool is generally used to make warm, medium to heavy weight fabrics for outer wear.

Acetate, as a general rule, (In my opinion), feels great, silky, and has a pleasing smell.

Wool, as a general rule, (IMO), is scratchy but warm, and smells like a wet sheep when wet.