When I came here from England in 1981 I found I needed to learn a new language in some respects!
Muslin in the US = cheesecloth in the UK, and cheesecloth in the UK = muslin in the US. Don't ask me why!
In 1981, muslin (the US version) was what everyone was using to back their quilts. It was softer than the front fabric, easier to quilt by hand and showed to advantage all that beautiful hand quilting. (!)