The simplest way to explain this is that cloud mining is cost-efficient, whereas remote (hosted) mining gives you more control.
Such a nice way to summarize it, while probably ignoring the majority of the issues. OP, don't get trapped by marketing words like this. Not saying they are lying, but there are dozens of businesses that scam their users in the end while promising cost-efficient mining. Even if they are honest, the risk outweighs the benefit.
FYI, your link doesn't work.