Let $R$ be a commutative ring, $\mathfrak p$ a prime ideal of $R$ and $M$ an $R$-module.
I've seen the terms 'localization' $M_\mathfrak p$ of $M$ and the completion $M_\mathfrak p$ at $\mathfrak p$ used with the same symbol.
My question is, is there any relationship between these two objects?
Many thanks for your help.