A "forerunner" is someone who did something first, earlier than others did something, or something that was the first general type of something that developed further into a somewhat different form later. But the focus of the word is on something happening earlier than other things. "The phonograph was the forerunner of the record player."
A "frontrunner" is someone who is in the first place of some race or contest. The contest or race could have happened in the past or could be happening in the present or could happen in the future ("possible frontrunner"). The focus is on the person (or thing, I guess)'s position in this race. They are in the front of the line in the race, so they are likely to win.