Detached lining, corset cover, they're all the same, other than all the picture's I've seen of corset covers they are usually pretty fancy. I left the cover until after the dress was done, which only left me a couple days to finish it. It's about as plain as it can be, but the fit is pretty good.
I bought the higher-grade muslin at Joanns thinking that would help the quality of the overall garment; I was sorely mistaken. I am not happy at all with the fabric, which feels exactly like the same $1 a yard stuff that I only use for mockups.
The first version of this corset cover had piped armscye's, but they were too tight. So I ripped off the piping and enlarged the armscye and sewed the sleeve back on without the piping. Shame on me, I know, but no one will ever see it.
Overall, I like the it, and it functions all right, but it is in need of some boning. Sometimes, it doesn't want to stay down, and will ride up after a while and cause funny lumps under the dress. This particular detached lining will probably eventually be replaced by a nicer, maybe fancier, one.