In my mind, the difference is that a bass player doesn't know the nuances or the techniques required of playing the bass well. This often applies to a guitarist who might pick up a bass for a recording, or who joins a band because they need a bass player but there's nobody else available.
A bassist, on the other hand, has spent time and effort to learn the ins and outs of the instrument and whether or not it's their primary instrument all the time, they are able to play at a high level and have all of the required fundamentals and gear to perform well.
I make a similar distinction between a painter and "someone who paints," a singer and "someone who sings", or more distinctly, a scientist and someone who reads a science news clipping.