"insist" and "persist"

To insist means to demand.

To be firm in a demand or course; refuse to yield: insisted on giving me a second helping.

http://dictionary.reference.com/browse/insist


To persist means to pursue a goal with resolute determination; refuse to stop.

1. To be obstinately repetitious, insistent, or tenacious.
2. To hold firmly and steadfastly to a purpose, state, or undertaking despite obstacles, warnings, or setbacks.
3. To continue in existence; last: hostilities that have persisted for years.

http://dictionary.reference.com/browse/persist