partial view from another view code example

Example: mvc view vs partial view

I think the biggest difference is about the use of the _Layout page:

PartialView(): the razor engine will get the view (e.g. index.cshtml) without any layout page (_layout.cshtml).
View(): the engine will get your view (e.g. index.cshtml) and then appends the content of this view inside the layout page (_layout.cshtml)