To simply say, content wrapper holds all visual elements and content on the page. Yes, it centers the content inside the <div> element which is conventionally used when using a content wrapper, but it's also opinionated.
This is normally achieved by using margins, and the most common way of using a content wrapper; eg:
.wrapper {
margin-right: auto;
margin-left: auto;
max-width: 960px;
// Or set a padding inside of the wrapper
padding-right: 10px;
padding-left: 10px;
}
Additionally, wrappers are also used for things like applying a sticky footer.
Otherwise, as for the difference between a container which may usually inherit the same properties, usually intends another kind of containment. One that sometimes necessary to implement a behavior or styling of multiple components.
It serves the purpose of grouping elements both semantically and visually.
The terms wrapper and container can also mean the same thing depending on the developer and what they intend. Just remember to use them in the right way.