Is there story continuity between various Need For Speed games?

The Need for Speed series as a whole does not have a continuous plot, but some games within the series do have storylines.

Several games such as Need for Speed Most Wanted (2005) and Need for Speed Most Wanted (2012) have the exact same game premise but there are no overlapping characters (in fact NFS:MW 2012 has no characters at all). They both share a goal of beating the top racers in the city and share a name, but the similarities stop there.

Other games like Need for Speed (2015) are set in a quasi-real world with real-life racing superstars making cameos. Others - like Need for Speed Payback - is set in a fully fictional world with fully fictional characters.

There are some games within the Need for Speed series which do share a plot, such as Need for Speed Underground 1 & 2, but they do not share a plot with the series as a whole.

To make things more confusing, some cars make repeat appearances throughout the franchise, almost becoming a character of their own. The iconic BMW M3 that made its debut on the cover of NFS Most Wanted (2005) has been ported into other games including NFS Carbon, NFS World, NFS Most Wanted (2012), NFS Edge, and NFS Heat.

In conclusion, there certainly is no overarching plot, but the games do have many small similarities that mark them as part of the same franchise.