A "contributory pension" is a pension to which an employee makes contributions from, a "noncontributory pension" is one where the entire amount is funded by the employer, which is a different axis of distinction from the pension (defined benefit) vs. defined contribution distinction.
Ah, this is the difference. For me (in the UK), a pension can be either defined benefit or defined contribution.
There are three positions on your contributory axis - noncontributory (employer pays all), contributory (employer and employee pay), and personal (completely independent of employer).