A web site is a destination in its own right. It is an end point for the visitor. The creators have built the site to keep you there.
A portal on the other hand is not a destination as such. Rather it is more like a bus terminus, signposting users onwards to other places. A portal differs from a web site in that it can be regarded more as a meeting place or gathering point for visitors to commence surfing to a set of pre-determined locations.
An example of a web site could, for example, be beer-widget.com, the company site of a beer widget-making company. A portal is a site like digital-stuff.com, a site that's dedicated to music, movies and online gaming.