Let $R$ denote a discrete valuation ring, so $Spec(R)$ consists of two points, the generic point and the special point. Now I am familiar with the definition of fibers as a fibered product when considering a morphism $X \rightarrow SpecR$ for a scheme $X$ and a point $p$ in $SpecR$. For the special fiber, we look at the special point of $SpecR$. But which morphism are we looking at? I've seen the term the special fiber lots of times. What is the special morphism corresponding to the special fiber?
I think I am missing something here..