Star time

If I've understood the general theory of relativity, gravity "slows" light, and thus also time. So for a star, is there a significant difference in time difference between the core and the "surface" and does this have anything to say for a star's workings?

How do you measure/count time for a star? Does our system based on 133Caesium half-life work (months/years/millenia)?

I'll try to be more specific; how long is a minute on earth's surface compared to a minute on Sol's surface. (Is it longer since there's a stronger gravitational forceon Sol?)