If you take the product you already built (your fixed point) and apply it to a different market, that's a pivot.
Pet Peave: If you rename your company and now it's doing something completely new with a new codebase, it's not a pivot, it's starting over!
Discontinuous jumps may be necessary, but don't pretend you are pivoting your idea. And like TFA said, you lose a lot of confidence from your employees and your investors if you are skittish and jumping all over the place. The founders, like the name implies, form the foundation. Shaky foundations don't build strong buildings.
It's possible for a small pivot to make a major different, it's also possible for a pirvot to be 180degrees, i.e. a complete turn around.
That said, I'm with you, it irks me when a company "pivots" and is basically a new company with the same people behind it - but from the point of view of the definition of "pivot", it does fit.
In my opinion, you're only starting over if you dissolve the legal entity, thus giving up the team and any funding they may have received.
The fixed point there is the team, and the knowledge they gained.