Smoothing splines have all the knots (knots at each point), but then regularizes (shrinks the coefficients/smooths the fit) by adding a roughness penalty term (integrated squared second derivative times a smoothing parameter/tuning parameter).
In one way, it's sort of analogous to a kind of "weighted" ridge regression, if you're prepared to regard the way the basis functions come into the penalty as weights.
Discrete versions of smoothing splines (which replace the integrated squared derivatives with summed squared differences) have a long history, dating back at least a century.